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HALL'S  MATHEMATICAL  SERIES  ''.' 


\  ,  A^  :    \\''^'UJl\l 


AN 


ELEMENTARY  AEITHMETIC 


ORAL  AND  WRITTEN 


FRANK    H.  HALL 

AUTHOR  OF  "THE   WERNER  ARITHMETICS,"    "THE  ARITHMETIC  READERS,"  J  STC. 


WERNER  SCHOOL  BOOK  COMPANY 

NEW  YORK        CHICAGO        BOSTON 


G  A  lA^ 


HALL'S  MATHEMATICAL  SERIES 


THE  WERNER  ARITHMETICS 

A     Three-Book   Course  for  -Graded  Schools 

Book  I.  For  third  and  fourth  grades,  cloth,  256  pages,  40c. 
Book  II.  For  fifth  and  sixth  grades,  cloth,  288  pages,  40c. 
Book  III.     For  seventh  and  eighth  grades,  cloth,  288  pages,  50c. 


TEACHERS'  HAND  BOOK 

giving  oral  work  preparatory  for  Book  I,  suggestions  to 
teachers  who  are  using  the  Werner  Arithmetics,  answers  to 
problems  in  Books  II  and  III,  and  a  large  amount  of  supple- 
mentary seat-work.     Cloth,  131  pages,  25c. 


THE  HALL  ARITHMETICS 

A    Tiiio-Book  Course  /or  Graded  or  Ungraded  Schools 
Hall's  Elementary  Arithmetic,  cloth,  248  pages,  ,  35c. 

Hall's  Complete  Arithmetic,  cloth,  448  pages,  ,  .      60c. 


Copyright,  1899 
By  WERNER  SCHOOL   BOOK  COMPANY 


Typography  by  R.  R.  Donnelly  Sons  Co.,  Chicago 


PREFACE. 

The  prominent  feature  of  this  book  is  the  spiral  advance- 
ment plan  upon  which  it  is  built.  The  basis  of  the  spiral 
is  the  five  fundamental  thought  processes  of  arithmetic, 
viz.: 

1.  The  uniting  of  numbers  (of  things) — addition. 

2.  The  separating  of  numbers  (of  things) — subtraction. 

3.  The  taking  of  numbers  (of  things)  a  given  number  of 
times — multiplication. 

4.  The  finding  of  how  many  times  one  number  (of 
things)  is  contained  in  another  number  (of  things) — ■ 
division. 

5.  The  finding  of  one  of  the  equal  parts  of  a  number  (of 
things) — division;  or,  as  it  is  sometimes  cslled,  partition. 

These  five  processes  appear  in  groups, — five  times  on 
page  9  in  problems  so  simple  that  the  tyro  will  find  little 
difficulty  in  understanding  them;  twice  on  page  10;  five 
times  on  page  11;  four  times  on  page  23;  twice  on  page 
25  ;  three  times  on  page  89  ;  twice  on  page  96;  three  times 
on  page  109  ;  twice  on  page  114 ;  three  times  on  page  119; 
twice  on  page  146,  and  at  least  once  on  nearly  one  fourth 
of  the  pages  of  the  book.  Each  of  these  "spirals"  is  a 
little  more  difficult  than  the  preceding  one,  and  each  is 
preparation  for  the  one  that  follows. 

The  variety  in  the  book  comes  (1)  from  the  introduction 
of  new  terms,  (2)  from  the  gradual  increase  in  the  difficulty 
of  the  problems,  and  (3)  from  the  different  magnitudes 
(things)  to  which  these  processes  are  applied. 

The  plan  of  the  book  provides  that  the  pupil  may 
become  familiar  with  the  terms  peculiar  to  mathematics 

54! 4 in 


'/,  /4v  '  PREFACE. 

cc  r  c  •by'l'Kfeit'iti^e  rather  taan  by  definition.     See  the  words  sum, 
"^'''  *'  di'ff evince,  product,  quotient, — pages  18,  19,  20,  21,  22,  156, 
157,  158,  159  ;  the  words  t7nangle,  ohlong,  x>entagon,  square, 
perimeter,  area, — pages  63,  73,  83,  93,  103,  113. 

On  pagiBS  10  and  12  the  fundamental  processes  are  applied 
to  inches,  feet,  and  yards;  on  page  23,  to  apples,  cents,  trees, 
and  degrees;  on  page  35,  to  halves  and  fourths;  on  page  36, 
to  half-inches  and  fourth-inches;  on  page  37,  to  half-dollars 
and  fourth- dollars ;  on  page  45,  to  halves  and  sixths;  on 
page  55,  to  halves,  fourths,  and  eighths;  on  page  89,  to 
inches,  sixths,  and  tenths  written  decimally,  etc. 

In  no  part  of  the  book  is  the  pupil  allowed  to  lose  sight 
of  the  fact  that  his  arithmetic  work  is  mainly  adding,  sub- 
tracting, multiplying,  dividing,  and  "parting";  and  he 
soon  learns  to  take  great  delight  in  applying  these  processes 
to  new  magnitudes. 

So  close  is  the  connection  between  the  oral  and  the 
written  work  (see  pp.  112,  122,  132,  142,  155,  156,  157, 
165,  170,  209,  etc.),  that  the  former  becomes  a  preparation 
for,  and  a  stepping  stone  to,  the  latter.  It  is  all  "mental " 
arithmetic,  some  of  the  problems  of  which  are  to  be  solved 
without  and  some  with  the  aid  of  a  pencil. 

There  is  such  an  abundance  of  concrete  problems  that 
the  pupil  never  leaves  out  of  his  thought,  for  any  consider- 
able length  of  time,  the  magnitude  idea.  But  if,  in  the 
learning  of  the  merely  mechanical  processes,  he  for  the 
moment  loses  sight  of  quantity,  he  is  able  quickly  to  pro- 
ject into  the  abstract  problem  the  notion  of  magnitude  and 
magnitude  relation.  The  book  thus  becomes,  not  simply 
an  arithmetic,  but  a  first  book  in  mathematics. 

F.  H.  H. 

Jacksonville,  Illinois,  April,  1899. 


NUMBER  FACTS 

To  be  taught  orally  before  the  book  is  put  into  the 
hands  of  the  pupil.  Each  fact  of  separation  or  combina- 
tion here  given  should  be  worked  out  with  objects  and 
measurements,  then  memorized — perfectly  memorized. 

THIRTY-THREE    FACTS    OF    ADDITIOX. 


1 

1 

2 
1 

3 
1 

2 
2 

4 

1 

3 

2 

5 

1 

4 
2 

3 
3 

6 
1 

5 
2 

2 

3 

4 

4 

5 

5 

6 

6 

6 

7 

7 

4 
3 

7 
1 

6 
2 

5 
3 

4 
4 

8 
1 

7 
2 

6 
3 

5 
4 

9 

1 

8 
2 

7 

8 

8 

8 

8 

9 

9 

9 

9 

10 

10 

7 
3 

6 
4 

5 
5 

9 
2 

8 
3 

7 
4 

6 
5 

9 
3 

8 
4 

7 
5 

6 
6 

10 

10 

10 

11 

11 

11 

11 

12 

12 

12 

12 

If  the  thirty-three  facts  of  addition  given  above  are 
taught  properly,  the  pupil  will,  at  the  same  time,  acquire  a 
knowledge  of  the  corresponding  facts  of  subtraction ;  thus, 
if  it  is  clear  to  the  pupil  that  7  and  5  are  12,  he  will  also 
know  that  12  less  7  are  5,  and  that  12  less  5  are  7. 

TWELVE    FACTS    OF    MULTIPLICATION. 


2  twos   =    4 

3  twos 

=    6 

4  twos     =  8 

5  twos    =10 

6  twos 

=  12 

2  threes  =  6 

3  threes  =    9 

4  threes 

=  12 

2  fours    =  8 

3  fours  =  12 

2  fives 

=  10 

2  sixes  =  12 

If  these  twelve  facts  of  multiplication  are  taught  prop- 
erly, the  pupil  will,  at  the  same  time,  acquire  a  knowledge 
of  twelve  facts  of  division ;  thus,  if  it  is  clear  to  him  that 
3  twos  are  6,  it  must  be  equally  clear  that  6  is  3  twos ;  or, 

5 


6  ELEMENTARY    ARITHMETIC. 

to  use  the  ordinary  mathematical  expression  of  this  fact, 
that  2  is  contained  in  6  three  times. 

These  twelve  facts  of  multiplication  will  also  give  to  the 
thoughtful  pupil  twelve  other  facts  of  division,  often  called 

FACTS    OF    PARTITION. 


1  of    4 

=  2         J  of    6  =  2 

i  of    8  =  2       i  of  10 

==  2 

lof  12 

^2         J  of    6  =  3 

i  of    9  =  3       J  of  12 

=  3 

iof    8 

=  4         J  of  12  =  4 

i  of  10  r=  5       i  of  12 

■=  6 

SEVEN    DENOMINATE 

NUMBER    FACTS. 

1  foot  =  12  inches.     3  feet  =  1  yard.       2  nickels  =  1  dime. 

10  dimes  =  1  dollar.    2  pints  =  1  quart.    4  quarts  =  1  gallon. 

100  cents  =  1  dollar. 

FACTS    OF    PARTITION    AND    MULTIPLICATION. 

4  is  f  of  6.  6  is  I  of  9.  8  is  |  of  12. 

6  is  f  of  8.  9  is  f  of  12.  4  is  f  of  10. 

It  will  be  observed  that  these  facts  are  combinations  of 
facts  given  before.  The  work  should  be  performed  first 
with  objects. 

It  is  very  desirable  that  the  pupil  shall  give  the  answer  to 
such  questions  as,  6  is  f  of  hoio  many?  not  from  memory,  but 
by  thinking  6  objects  divided  into  two  equal  groups,  and  by 
adding  to  the  two  groups  another  similar  group :  thus,  (111 
111)  111. 

OTHER    FACTS    OF    PARTITION. 

i  of  3  =  If  J  of  5  =•  2^.  i  of  7  =  31. 

i  of  9  =  4L.  i  of  11  =  B\.  i  of  7  =  21 

Not  by  definition,  but  by  frequent  use,  the  pupil  should 
become  familiar  with  the  following  terms  and  expressions : 
add,  subtract,  multiply,  divide,  sum,  difference,  product,  quotient, 
square,  oblong,  triangle,  square  inch,  2-inch  square,  3-inch 
square,  is  contained  in. 

Do  not  use  the  sign  (x)  for  the  word  times.  Whenever  this 
sign  is  employed  in  the  lower  grades,  it  should  be  used  for  the 
words  multiplied  by. 


CONTENTS. 


PRIMARY  NUMBER  PACTS 

PAGES 

Outline  of  work  to  be  done  orally 5,6 

PART   I. 

Primary  Number  Pacts  applied  to  linear  magnitudes, — 
inch,  foot,  yard;  to  magnitudes  of  capacity,— pm^, 
quart;  to  magnitudes  of  value, — cent,  nickel,  dime, 
dollar;  to  magnitudes  of  time, — day,  week;  to  sur- 
face magnitudes, — 1-inch  square,  2-inch  square,  3-inch 
square ;  to  fractional  units, — half,  third,  fourth ;  to 
inexact  units  of  measurement, — apple,  ball,  egg,  pie, 
tree,  etc 9-40 

PART  II. 

Primary  Number  Facts 41,  51,  61,  71,  81,   91,  etc 

Primary  Number  Pacts  applied  to  a  variety  of  magni- 
tudes   42,  52,  62,  72,  82,   92,  etc. 

Primary  Number   Pacts   applied   to   linear   and   surface 

measurements 43,  53,  63,  73,  83,   93,  etc. 

Miscellaneous  Problems 44,  54,  64,  74,  84,    94,  etc. 

Common  Fractions 45,  55,  65,  75,  85,   95,  etc. 

Common  Fractions  applied  to  a  variety  of  magnitudes, 

46,  56,  66,  76,  86,   96,  etc. 

Denominate  Numbers 47,  48,  57,  58,  68,  78,      88,  98 

Miscellaneous  Problems 49,  50,  59,      60,  79 

Adding  by  2's,  3's,  4's,  etc 67,  77,  87,  97, 107,  117,  etc. 

Tenths  written  decimally 70,  80,  90 

The  meaning  of  certain  arithmetical  expressions .  89, 99, 109,  119, 129 

Time  Problems 100, 110,114,  120,  124,  130,  134,  140, 144 

Review 147,  149, 152 

7 


8  ELEMENTARY    ARITHMETIC. 

PART   III. 

PAGES 

Decimals — tenths 153-172 

Denominate  Numbers 174, 184 

Fractions 175,  176, 177;  185,  186, 187 

Surface  Measurements 178,  179;  188, 189 

Ratio  and  Proportion 180,  181;  190, 191 

Miscellaneous  Problems ,  182, 192 

PART  IV. 

Decimals -hundredths 193-212 

Terms  in  multiplication  and  division 213, 223 

Denominate  Numbers ; 214, 224 

Fractions 215,  216;  225, 226 

Miscellaneous  Problems 217,  222,  227 

Surface  Measurements 218,  219;  228,  229 

Ratio  and  Proportion 220,  221 

Problems  in  Addition,  Subtraction,  Multiplication,  and 

Division 230,  231,  232 

Definitions  and  Explanations 233-240 

Suggestions  to  Teachers .  241-248 

PROBLEMS 

At  bottom  of  pages,  beginning  with  p.  11. 

Addition pp.  11,  16,  21,  26,  31,  36,  etc. 

Subtraction pp.  12,  17,  22,  27,  32,  37,  etc. 

Multiplication pp.  13, 18,  23,  28,  33,  38,  etc. 

Division pp.  14,  19,  24,  29,  34,  39,  etc. 

Division  ("  Partition  ") pp.  15,  20,  25,  30,  35,  40,  etc. 


^  ■>     ■>  i  ■> 
,  l'  J  1    J 


J     5    ,    3   o      e » 


ARITHMETIC. 


PAET   I. 


•••«     •• 


1.  Four  and  two  are  . 

2.  Five  less  two  are  .  •••oo 

3.  Three  times  two  are  .  *•  ** 

4.  Six  is  twos.  ••  •• 

5 .  One  half  of  six  is  . 


•••  ••• 

6.  Five  and  three  are  .  5  and  3  = 

7.  Seven  less  four  are  .  7  less  4  = 

8.  Four  times  two  are  .  4  times  2  = 

9.  Eight  is  twos.  8  is  2's. 

10.  One  half  of  four  is  .         |  of  4  = 

11.  William   earned    5    cents    and   his    brother 
earned  6  cents;  together  they  earned  cents. 

12.  James  had  12  cents;   he  gave  his  sister  4 
cents;  he  then  had  cents. 

13.  John  paid  2  cents  each  for  5  pencils;  for  all 
he  paid  cents. 

14.  Harry  has  10  cents;    oranges  cost  5  cents 
each ;  he  can  buy  oranges . 

15.  Richard   paid    8    cents   for   2    lemons;  one 
lemon  cost  cents. 

9 


JO  KL.EMENTARY    ARITHMETIC. 


One  fourth  of  a  foot. 

1.  Tioelve  inches  are  one  foot. 

2.  Six  inches  are of  a  foot. 

3.  Three  inches  are of  a  foot. 

4.  One  half  of  a  foot  and  2  inches  = 

5.  One  half  of  a  foot  less  2  inches  = 

6.  Three  times  2  inches  are  inches. 

7.  2  inches  are  contained  in  8  inches times. 

8.  One  half  of  6  inches  is  inches. 

9.  Mary's  pencil  is  3  inches  long;  Alice's  pen- 
cil is  4  inches  long;  together  they  are  inches 

long. 

10.  Jane  had  a  pencil  8  inches  long ;  she  broke 

off  a  piece  2  inches  long ;  what  remained  was  

inches  long. 

11.  Think  of  a  square.    A  square  has sides. 

One  side  of  a  2-inch  square  measures  inches. 

All  the  sides  of  a  2-inch  square  together  measure 
inches. 

12.  Ann  had  a  piece  of  ribbon  10  inches  long; 

she    cut   it   into   2-inch   pieces;    there  were  

pieces. 

13.  I  am  thinking  of  a  square.     It  has  

equal  sides.     All  its   sides   together  measure    12 
inches.     It  is  a  inch  square. 


PAKT  I, 


11 


1.  Ten  and  two  are  — 

2.  Ten  less  two  are  — 

3.  Three  times  ten  are 

4.  Forty  is  tens. 

5.  One  half  of  forty  is 


10  and  3  = 

-.     10  less  4  = 

.     5  times  10  = 

60  is  lO's. 

.     10  is  1  of 


6.  Twenty  and  10  are  — 

7.  Twenty  less  2  are  

8.  Four  times  10  are  — 

9.  Seventy  is  tens. 

10.  One  third  of  30  is  


-.     20  and  20  = 
.     30  less  2  = 
6  times  10  — 

50  is  lO's. 

.     t  of  30  = 


11.  A  boy  paid  2  dimes  for  a  slate  and  3  dimes 
for  a  book;  for  both  he  paid  cents. 

12.  The  price  of  Susie's  book  was  38  cents;  she 
gave  the  salesman  4  dimes ;  she  should  receive  in 
change  cents. 

13.  At  10  cents  a  yard,  2  yards  of  ribbon  cost 
cents;   one  half  of  a  yard  costs  cents; 


two  and  one  half  yards  cost  cents. 

14.  For  some  railroad  tickets  I  paid  60  cents; 
each  ticket  cost  10  cents;  there  were tickets. 

15.  For  4  melons  James   j^aid  40   cents;    one 

melon  cost  cents.     One  fourth  of  40  cents  is 

cents. 


(1)  Read,  and  give  sums.     (2)  Copy  and  add. 

20  21  23  22  22 

4  4  4  6  2 


28 

2 


12 


ELEMENTARY    ARITHMETIC. 


1.  One  foot  is 


inclies. 


2.  Two  feet  are  24  inches. 

3.  Three  feet  are  36  inches. 

—  feet. 

—  inches. 


4.  One  yard  is 
One  yard  is 


5. 
6. 


One  half  of  a  yard  is  

7.  One  third  of  a  yard  is  — 

8.  Two  thirds  of  a  yard  are 


9.  Six  inches  and  6  inches  are  inches. 

10.  One  foot  less  6  inches  are  inches. 

11.  Fonr  times  3  inches  are  inches. 

12.  3  inches  are  contained  in  12  inches  — 
times. 

13.  One  third  of  twelve  inches  is  inches. 


14.  Two  feet  and  2  inches  are 

15.  One  yard  less  2  inches  are 


inches, 
inches. 


16.  Think  of  a  line  6  feet  Ions;.     Six  feet  are 


yards.     Nine  feet  are 


17.  One  yard  and  1  foot  are  — 

18.  One  yard  and  2  feet  are  — 

19.  Seven  feet  are  yards  and 


yards. 

—  feet. 

—  feet. 


foot. 


20.  Three  times  2  feet  are  feet,  or 

yards. 

21.  Two  12's  are  .     Three  12's  are  - 


(1)  Kead,  and  give  differences.      (2)  Copy  and  subtract. 

26  28  29  25  27  30 

4  3  6  4  7  2 


PART    I. 


J3 


A  1-inch 
Square. 


1.  Think  of  a  2-incli  square.  Think  of  a  2-inch 
square  divided  into  1-inch  squares.  A  2-inch  square 
is  equal  to  1-inch  squares. 

2.  Think  of  a  3-inch  square.  Think  of  a  3-inch 
square  divided  into  1-inch  squares.  A  3 -inch  square 
is  equal  to  1-inch  squares. 

3 .  Think  of  an  oblong  1  inch  wide  and  4  inches 
long.     Think  of  this  oblong  divided  into   1-inch 

squares.     Such  an  oblong  is  equal  to  1-inch 

squares. 

4.  An  oblong  2  inches  wide  and  4  inches  long 
is  equal  to  1-inch  squares. 

5.  An  oblong  2  inches  wide  and  3  inches  long 
is  equal  to  1-inch  squares. 

6.  An  oblong  2  inches  wide  and  5  inches  long 
is  equal  to  1-inch  squares. 

7.  One  fourth  of  a  2-inch  square  = 

8.  One  half  of  a  2-inch  square  = 

(1)  Eead,  and  give  products.     (2)  Copy  and  multiply. 

20  12  21  32  34  35 

2  2  2  2  2  2 


14 


ELEMENTARY    ARITHMETIC. 


1.  Four  times  2  balls  are 


balls. 


2.  2  balls  are  contained  in  8  balls 


times. 


3.  Three  times  3  tops  are  tops. 

4.  3  tops  are  contained  in  9  tops  


*  *  •  • 


times. 


*  *  *  * 


5.  Two  times  4  stars  are 


stars. 


6.  4  stars  are  contained  in  8  stars 


times. 


•    • 


•    •    • 


•    •    • 


7.  Four  times  3  dots  are 


dots. 


8.  3  dots  are  contained  in  12  dots 


•    •    • 


times. 


9.  Five  times  2  eggs  are  — 
10.  2  eggs  are  contained  in  10  eggs 


eggs. 


11.  Three  times  4  hats  are 


hats. 


12.  4  hats  are  contained  in  12  hats 


times. 


times. 


(1)  Eead,  and  give  quotients.     (2)  Copy  and  divide. 
2  balls)12  balls  2  stars)20  stars 


2)40 


—  times 
2)42  2)44 


—  times 
2)46  2)48 


PART  I.  15 

1.  One  half  of  4  cents  is  cents. 

2.  Two  cents  are  contained  in  4^  times. 

3.  One  half  of  6  cents  is  cents. 

4.  Two  cents  are  contained  in  6^  times. 

5.  One  half  of  8  cents  is  cents. 

6.  Two  cents  are  contained  in  8^  times. 

7.  One  half  of  10  cents  is  cents. 

8.  Two  cents  are  contained  in  10^  times. 

9.  One  half  of  12  cents  is  cents. 

10.  Two  cents  are  contained  in  12^  times. 

11.  One  half  of  20  cents  is  cents.. 

12.  Two  cents  are  contained  in  20^  times. 

13.  One  half  of  40  cents  is  cents. 

14.  Two  cents  are  contained  in  40^  times. 

15.  One  liaK  of  60  cents  is  cents. 

16.  Two  cents  are  contained  in  60^  times. 

17.  One  half  of  80  cents  is  cents. 

18.  Two  cents  are  contained  in  80^  times. 

(1)  Eead,  and  give  quotients.     (2)  Copy  and  divide. 

2)12  cents  2)14  cents  2)20  cents 

—  cents  —  cents  —  cents 

2)24^'         2)26^         2)28j^         2)80^         2)40^ 


16 


ELEMEKTABY    AKITHMETIC. 


1  pint. 


1  quart. 


1.  Two  pints  are  one  quart. 

2.  Six  pints  are  quarts. 

3.  Two  quarts  are  pints. 

4.  Six  quarts  are  pints. 

5.  Four  quarts  are  pints. 

—  quarts. 

—  quarts. 

—  pints. 


6.  Four  pints  are  — 

7.  Ten  pints  are  — 

8.  Ten  quarts  are  — 

9.  Mr.  Smith  sold  1  pint  of  milk  to  each  of  4 
customers ;  to  all  he  sold  quarts. 

10.  At  3  cents  a  pint^  one  quart  of  milk  costs 


11.  At  4  cents  a  quart,  one  pint  of  milk  costs 


12.  At  4  cents  a  quart,  two  quarts  and  one  pint 
of  milk  cost  cents. 

13.  2   quarts  are  contained  in   6   quarts  

times. 

14.  1  pint  is  contained  in  3  quarts  times. 

(1)  Eead,  and  give  sums.     (2)  Copy  and  add. 

28  28  28  38  38  38 

3  4  5  2  3  4 


PART     1.  17 

1.  One  third  of  6  balls  is  balls. 

2.  Two  thirds  of  6  balls  are  balls. 


3.  One  third  of  9  balls  is  balls. 

4.  Two  thirds  of  9  balls  are  balls. 

5.  Arrange  12  balls  so  that  it  will  be  easy  to 
think  the  number  of  balls  in  one  third  of  12  balls, 
and  the  number  of  balls  in  two  thirds  of  12  balls. 

6.  One  third  of  12  balls  is  balls. 

7.  Two  thirds  of  12  balls  are  balls. 

••••  ••    ••    oo 

8.  Four  balls  are  two  thirds  of  balls. 


••••••  •••    •••    ooo 

9.  Six  balls  are  two  thirds  of  balls. 

10.  Arrange  8  balls  so  that  it  will  be  easy  to 
think  the  number  of  balls  of  which  8  balls  are  two 
thirds. 

11.  Eight  balls  are  two  thirds  of  balls. 

— .  1  of  9  is  . 

— .  i  of  12  is  . 

— .  10  is  1  of  . 

— .  6  is  i  of  . 

(1)  Read,  and  give  differences.       (2)  Copy  and  subtract. 

30  40  50  30  40  50 

3  3  3  4  4  4 


12. 

|-  of    6  is 

13. 

i  of    8  is 

14. 

i  of  10  is 

15. 

A  of    6  is 

18  ELEMENTARY   ARITHMETIC. 

1.  The  sum  of  7  and  4  is  . 

2.  The  sum  of  20  and  6  is  . 

3.  The  sum  of  21  and  4  is  . 

4.  The  sum  of  32  and  4  is  . 

5.  The  sum  of  43  and  2  is  . 

6.  Peter  and  Harry  together  had  12  marbles; 
Harry  had  7 ;  Peter  had  . 

7.  The  sum  of  two  numbers  is  8;  one  of  the 
numbers  is  5 ;  the  other  number  is  . 

8.  Joseph  has  a  new  bicycle.  There  is  a 
cyclometer  on  it.  When  Joseph  had  used  the 
bicycle  two  days  the  cyclometer  showed  that  he 
had  ridden  11  miles;  he  rode  5  miles  the  first  day; 
the  second  day  he  rode miles. 

9.  The  sum  of  two  numbers  is  10;  one  of  the 
numbers  is  6 ;  the  other  number  is  . 

10.  Joseph  rode  8  miles  in  the  morning  and  4 
miles  in  the  afternoon ;    in  all  he  rode  miles. 

11.  Mary  paid  6^  for  2  thirds  of  a  yard  of  rib- 
bon;  at  the  same  rate,  1  yard  would  cost  

cents. 

12.  ^  of  6  is  .  6  is  i  of  -. 

13.  f  of  6  are  .  6  is  f  of  . 

14.  1  of  3  is  .  3  is  i  of  . 

15.  I  of  9  are  .  8  is  f  of  . 


(1)  Eead,  and  give  products.     (2)  Copy  and  multiply. 

25  35  45  21  22  23 

2  2  2  3  3  3 


PART  I.  19 


1.  The  difference  of  6  and  4  is  — 

2.  The  difference  of  12  and  8  is  - 

3.  The  difference  of  5  and  9  is  — 

4.  The  difference  of  26  and  24  is 

5.  The  difference  of  27  and  30  is 

6.  The  difference  of  35  and  40  is 


7.  The  temperature  at  9  o'clock  in  the  morning 
was  65  degrees  above  zero;  at  noon  it  was  75 ,-  the 
difference  was  degrees. 

8.  The  temperature  inside  the  schoolroom  was 
70  degrees  above  zero;  outdoors  it  was  50;  the 
difference  was  degrees. 

9.  The  temperature  at  noon  was  80  degrees 
above  zero;  at  4  o'clock  in  the  afternoon  it  was  10 
degrees  lower ;  at  4  o'clock  it  was  . 

10.  The  greater  of  two  numbers  is  90;  their 
difference  is  10 ;  the  less  number  is  . 

11.  The  temperature  at  10  o'clock  was  85  de- 
grees above  zero;  at  noon  it  was  10  degrees  higher; 
at  noon  it  was  . 

12.  The  less  of  two  numbers  is  55;  their  differ- 
ence is  10;  the  greater  number  is  . 

(1)  Eead,  and  give  quotients.     (2)  Copy  and  divide. 

3  dollars)  12  dollars         4  cents)  12  cents 
—  times  —  times 

3)15  3)33  3)36  3)39  3)63 


20  ELEMENTARY    ARITHMETIC. 

1.  The  product  of  4  and  2  is  — 

2.  The  product  of  6  and  2  is  ■ 

3.  The  product  of  5  and  2  is  

4.  The  product  of  3  and  4  is  

5.  The  product  of  3  and  2  is  


6.  The  product  of  10  and  2  is  . 

7.  The  product  of  20  and  2  is  . 

8.  I  have  an  orchard  in  which  there  are  four 
rows  of  trees;  in  each  row  there  are  10  trees;  in 

all  there  are trees.     4  tens  are .     5  tens 

are  . 

9.  The  length  of  one  side  of  a  3-inch  square  is 

inches;  the  length  of  all  its  sides  together  is 

inches.     4  threes  are  .      3  threes  are 

.     2  threes  are . 


10.  The  product  of  two  numbers  is  8;   one  of 
the  numbers  is  2 ;  the  other  number  is  . 

11.  The  product  of  two  numbers  is  40;  one  of 
the  numbers  is  2 ;  the  other  number  is  . 

12.  Ten  and  ten  and  ten  are  .     Three  tens 

are  .     The   product   of    3    and    10    is  . 

Twenty  is  the  product  of  10  and  .     Forty  is 

the  product  of  10  and  . 

(1)  Eead,  and  give  quotients.     (2)  Copy  and  divide. 
3)12  dollars  3)15  dollars  3)36  dollars 

—  dollars  —  dollars  —  dollars 

3)18  3)39  3)60  3)63  3)66 


PART   I.  21 

1.  The  quotient  of  6  divided  by  2  is  . 

2.  The  quotient  of  8  divided  by  4  is  . 

3.  The  quotient  of  10  divided  by  2  is  . 

4.  The  quotient  of  12  divided  by  3  is  . 

5.  The  quotient  of  12  divided  by  6  is  ■ . 


6.  The  quotient  of  20  divided  by  10  is  . 

7.  The  quotient  of  40  divided  by  4  is  . 

8.  I  have  an  orchard  in  which  there  are  60 
trees ;  these  trees  are  in  6  equal  rows ;  in  each  row 
there  are  trees.     Sixty  divided  by  6  equals 


9.  Edward  paid  60  cents  for  6  pounds  of  nuts; 
one  pound  cost  .     One  sixth  of  60  is  . 

10.  Byron  sold  papers  for  which  he  received  40 
cents;  he  sold  the  papers  at  2  cents  each;  he  sold 

papers.     Two  cents  are  contained  in  40  cents 

times. 

11.  One  half  of  12  is  .     2  is  contained  in 

12  times. 

12.  One  half  of  20  is  .     2  is  contained  in 

20  times. 

13.  One  third  of  12  is  .     3  is  contained  in 

12  times. 

14.  One  half  of  60  is  .     2  is  contained  in 

60  times. 

(1)  Read,  and  give  sums.     (2)  Copy  and  add. 

26     26     35     47     17     52 
10     20     20     20     20     20 


22  ELEMENTARY    ARITHMETIC. 

1.  The  sum  of  6  and  2  is  . 


2.  The  difference  of  6  and  2  is 

3.  The  product  of  6  and  2  is 


4.  The  quotient  of  6  divided  by  2  is 

5.  The  sum  of  40  and  20  is  . 


6.  The  difference  of  40  and  20  is 

7.  The  jDroduct  of  20  and  2  is 


8.  The  quotient  of  20  divided  by  2  is 

9.  The  sum  of  30  and  20  is  . 


10.  The  difference  of  30  and  20  is 

11.  The  product  of  30  and  3  is  - — 


12.  The  quotient  of  30  divided  by  3  is 

13.  The  sum  of  27  and  3  is  . 

14.  The  difference  of  27  and  3  is  

15.  The  product  of  12  and  2  is 


16.  The  quotient  of  12  divided  by  2  is 

17.  The  sum  of  30  and  5  is  . 


18.  The  difference  of  30  and  5  is 

19.  The  product  of  10  and  5  is 


20.  The  quotient  of  10  divided  by  5  is 

21.  One  half  of  3  feet  is  . 

22.  One  half  of  5  apples  is  . 

23.  One  half  of  7  inches  is  . 


(1)  Eead,  and  give  differences.       (2)  Copy  and  subtract. 

30     35     52     44     57     63 
10     10     10     20     20     20 


PART  I.  23 

1.  Six  apples  and  3  apples  are  apples. 

2.  Seven  apples  less  2  apples  are  apples. 

3.  Three  times  2  apples  are  apples. 

4.  Three  apples  are  contained  in  9  apples . 

5.  One  half  of  7  apples  is  apples. 

6.  Eight  cents  and  3  cents  are  cents. 

7.  Nine  cents  less  2  cents  are  cents. 

8.  Four  times  3  cents  are  cents. 

9.  Four  cents  are  contained  in  12  cents  . 

10.  One  third  of  12  cents  is  cents. 

11.  Twenty  trees  and  7  trees  are  trees. 

12.  Twenty  trees  less  2  trees  are  trees. 

13.  Two  times  20  trees  are  trees. 

14.  Two  trees  are  contained  in  40  trees  . 

15.  One  half  of  60  trees  is  trees. 

16.  Sixty-eight  degrees  and  4  degrees  are  . 

17.  Sixty-eight  degrees  less  4  degrees  are  . 


18.  Four  times  20  degrees  are  degrees. 

19.  Two  degrees  are  contained  in   12   degrees 


20.  One  third  of  30  degrees  is  degrees. 

21.  i  of  4  is  .  4  is  i  of  . 

22.  1  of  3  is  .  3  is  i  of  . 

23.  i  of  5  is  .  5  is  1  of  . 


(1)  Kead,  and  give  products.     (2)  Copy  and.  multiply. 

31  32  33  11  12  13 

3  3  3  3  3  3 


24 


ELEMENTARY   ARITHMETIC. 


1.  In  6  there  are  - 

2.  In  7  there  are  - 

3.  In  8  there  are  - 

4.  In  9  there  are  - 

5.  In  10  there  are 

6.  In  11  there  are 

7.  In  8  there  are  - 

8.  In  9  there  are  - 

9.  In  10  there  are 

10.  In  11  there  are 

11.  In  10  there  are 

12.  In  12  there  are 

13.  In  9  there  are  - 

14.  In  11  there  are 

15.  In  23  there  are 

16.  In  35  there  are 

17.  In  21  there  are 

18.  In  41  there  are 


19.  One  half  of  20  is 

20.  One  half  of  40  is 

21.  Onehalf  of  50  is 

22.  One  half  of  60  is 


—  twos. 

--  twos  and 

—  twos. 

—  twos  and 


-  twos. 

-  twos  and 

fonrs. 
fours  and  - 

-  fours  and 

-  fours  and 

-  fives. 

-  fives  and 


threes. 

-  threes  and 

-  tens  and  - 

-  tens  and  - 
twos  and  - 

-  twos  and  - 


of  21 


1 

1  of  41  = 
1  of  51  = 
i  of  61  = 


(1)  Eead,  and  give  quotients.     (2)  Copy  and  divide. 
4  apples)  12  apples  5  cents) 25  cents 


5)20 


—  times 
5)30  5)35 


■ —  times 
3)69  2)64 


PART  I.  25 

1.  John  had  22  cents,  and  his  mother  gave  him 
5  cents  more ;  he  then  had  cents. 

2.  AYilliam  had  36  cents;  he  spent  5  cents;  he 
then  had  cents. 

3.  David  paid  20  cents  each  for  2  books;  the 
books  cost  cents. 

4.  George  paid  50  cents  for  some  tablets;  the 
price  of  the  tablets  was  10  cents  each;  there  were 

tablets. 

5.  Harry's  new  drawing-pencils  cost  40  cents; 
there  were  4  of  them ;  each  pencil  cost cents. 

6.  In  one  coop  there  were  21  little  chickens; 
in  another  coop  there  were  8 ;  in  both  there  were 

chickens. 

7.  Susan  had  36  chickens;  4  of  them  died;  she 
then  had  chickens. 

8.  In  each  of  three  coops  there  were  20  chick- 
ens; in  all  there  were  chickens. 

9.  Mrs.  Brown  has  36  chickens  equally  divided 

among  3  mother  hens;    each  hen  cares  for  

chickens. 

10.  Mrs.  Harris  had  30  chickens;  she  divided 
them  equally  and  put  them  into  3  coops;  in  each 
coop  there  were  chickens. 

(1)  Read,  and  give  quotients.     (2)  Copy  and  divide. 

2)$14        2) $42        2) $44        2) $46         2)  $48 
2)24  2)26  2)28  2)62  2)64 


26  ELEMENTARY    ARITHMETIC. 

1 .  If  one  quart  of  milk  is  worth  6  centSj  1  pint 
is  worth  cents. 

2.  When  milk  costs  4  cents  a  quart,  1  pint 

costs  cents ;    1  quart  and  1  pint  cost 

cents;  2  quarts  cost cents;   2  quarts  and  1 

pint  cost  cents. 

3.  When  milk  costs  6  cents  a  quart,  9  cents 
will  pay  for  . 

4.  When  milk  costs  4  cents  a  quart,  6  cents 

will   pay   for  ;    10    cents   will   pay   for 

;  12  cents  will  pay  for . 

5.  When  milk  costs  6  cents  a  quart,  12  cents 
will  pay  for  . 

6.  Herbert  paid  6  cents  for  a  ball,  and  half  as 

many  cents  for  an  orange;   the  orange  cost  

cents;    the    orange    and    the    ball    together   cost 
.     The  sum  of  6  and  3  is  . 

7.  Four  two-cent  stamps  cost  cents. 

8.  Two  four-cent  stamps  cost  cents. 

9.  George  had  11  cents;  he  bought  3  two-cent 
stamps ;  he  then  had  cents. 

10.  My  j)en-holder  cost  8  cents;  my  pencil  cost 
half  as  much  as  my  pen-holder;    my  pencil  cost 

cents;    my  pen-holder  and  pencil   together 

cost  cents. 

(1)  Bead,  and  give  sums.     (2)  Copy  and  add. 

30     40     20     50     60     70 
15     12     17     14     13     18 


PART  I.  27 

1 .  William  had  six  cents ;  lie  paid  one  third  of 
his  money  for  a  tablet;  he  then  had  cents. 

2.  Jane  had  six  cents;  she  paid  two  thirds  of 
her  money  for  an  orange;  she  then  had cents. 

3.  Henry  earned  some  money;  he  spent  one 
half  of  what  he  earned  and  had  5  cents  left;  he 
earned cents ;  he  spent  cents. 

4.  James  earned  some  money;  he  spent  two 
thirds  of  what  he  earned  and  had  3  cents  left; 
he  earned  cents;  he  spent  cents. 

5.  Peter  earned  some  money;  he  spent  one 
third  of  what  he  earned  and  had  6  cents  left;  he 
earned  cents;  he  spent  cents. 

6.  A  hen  came  off  her  nest  with  a  nice  brood 
of  chicks;  but  there  came  a  rain  storm  and  three 
fourths  of  them  were  drowned;  the  poor  hen  then 
had  only  three  chicks ;  she  came  off  her  nest  with 
chicks;  the  rain' killed  chicks. 

7.  Mary  had  a  whole  family  of  dolls;  she  gave 
away  three  fourths  of  them  and  had  only  2  dolls 

left ;  before  she  gave  any  away  she  had dolls; 

she  gave  away  dolls. 

(1)  Read,  and  give  differences.     (2)  Copy  and  subtract. 

30     40     50     30     40     60 
12     12      12     13     13     13 


35 

45 

55 

35 

45 

55 

12 

12 

12 

13 

13 

13 

28  ELEMENTARY    ARITHMETIC. 

1.  One  half  of  4  apples  is  apples. 

2.  Four  apples  are  one  half  of  apples. 

3.  One  half  of  6  oranges  is  oranges. 

4.  Six  oranges  are  one  half  of  oranges. 

5.  One  half  of  three  toothpicks  is  . 


6.  Three  toothpicks  are  one  half  of  . 

7.  One  half  of  5  inches  is  inches. 

8.  Five  inches  are  one  half  of  inches. 

9.  One  half  of  7  square  inches  is  . 

10.  One  half  of  8  square  inches  is  . 

11.  One  half  of  9  square  inches  is  . 

12.  One  half  of  10  square  inches  is  . 

13.  One  third  of  three  blocks  is  block. 

14.  Three  blocks  are  one  third  of  blocks. 

15.  One  third  of  6  balls  is  balls. 

16.  One  third  of  9  balls  is  balls. 

17.  One  third  of  12  balls  is balls. 

18.  One  fourth  of  8  boys  is  boys. 

19.  One  fourth  of  12  boys  is boys. 

20.  One  fifth  of  10  girls  is  girls. 

21.  Two  fifths  of  10  girls  are  girls. 

22.  One  sixth  of  12  hats  is  hats. 

(1)  Kead,  and  give  products.     (2)  Copy  and  multiply. 
30  40  50  60  20  30 

2  2  2  2  3  3 


PART   I.  29 


1.  I  obtain  a  sum  by  

2.  I  obtain  a  difference  by 

3.  I  obtain  a  product  by  - 

4.  I  obtain  a  quotient  by  - 


5.  The  answer  in  addition  is  a  

6.  The  answer  in  subtraction  is  a  — 

7.  The  answer  in  multiplication  is  a 

8.  The  answer  in  division  is  a  . 


9.  The  sum  of  8  and  2  is 


10.  The  difference  of  8  and  2  is 

11.  The  product  of  8  and  2  is 


12.  The  quotient  of  8  divided  by  2  is  . 

13.  When  I  put  two  numbers  together,  I  . 

14.  When  I  take  one  number  from  another,  I 


15.  When  I  take  a  number  a  certain  number  of 
times,  I  . 

16.  When  I  find  how  many  times  one  number  is 
contained  in  another,  I  . 

17.  When  I  find  a  certain  part  of  a  number,  as 
one  half  of  it,  or  one  third  of  it,  or  one  fourth  of 
it,  I  . 

(1)  Eead,  and  give  quotients.     (2)  Copy  and  divide. 

$2)$12   $2)$2Q   $2)$24   $2)$26   $2)$28 
2)14     2)22     2)18     2)40     2)42 


30  ELEMENTAKY   ARITHMETIC . 

1.  2)6 

Two  apples  are  contained  in  6  apples  

One  half  of  6  apples  is . 

2.  3)12 

Three  dollars  are  contained  in  12  dollars 
One  third  of  12  dollars  is . 

3.  4)12 

Four  cents  are  contained  in  12  cents  

One  fourth  of  12  cents  is . 


4.  5)10 

Five  oranges  are  contained  in  10  oranges 
One  fifth  of  10  oranges  is . 

5.  6)12 

Six  inches  are  contained  in  12  inches  — 
One  sixth  of  12  inches  is . 

6.  4)40 

Four  cents  are  contained  in  40  cents  

One  fourth  of  40  cents  is  . 


7.     2)24 

Two  peaches  are  contained  in  24  peaches  ■ . 

One  half  of  24  peaches  is  . 

One  third  of  24  peaches  is . 

(1)  Read,  and  give  quotients.     (2)  Copy  and  divide. 
2)22  ft.      3)36  ft.     2)44  ft.      3)66  ft.     2)28  ft. 


IS 


PART  I.  31 

1.  One  half  of  1  quart  is . 

2.  One  half  of  1  foot  is  — —  inches. 

3.  One  half  of  1  yard  is . 

4.  One  half  of  1  dollar  is  cents. 

5.  One  half  of  1  dime  is . 

6.  One  half  of  7  quarts  is  . 

7.  One  half  of  a  2-inch  square  is  . 

8.  One  half  of  a  3-inch  square  is  . 

9.  One  half  of  5  feet  is . 

10.  One  half  of  an  oblong  2  inches  by  4  inches 


11.  Two  quarts  are  one  third  of 

12.  Four  inches  are  one  third  of- 

13.  One  foot  is  one  third  of  


14.  Three  inches  are  one  fourth  of  

15.  Twenty-five  cents  are  one  fourth  of 

16.  One  pint  is  one  fourth  of . 

17.  One  dime  is  one  third  of . 

18.  One  quart  is  one  fourth  of  


2 


19.  ^  of    4  is  .  4  is  i-  of 

1  of  9  is 


20.  1  of    6  is 

21.  i  of    8  is 

22.  i  of  10  is 

23.  i  of  12  is 


i  of  12  is 
10  is  i  of 
12  is  i  of 


(1)  Read,  and  give  sums.     (2)  Copy  and  add. 

30     30     30     20     20     20 
22     23     24     23     24     25 


32 


ELEMENTARY   ARITHMETIC. 


1. 
2. 
3. 
4. 
5. 
6. 


Two  is  one  fourth  of . 

Four  is of  eight. 

Six  is of  eight. 

Three  is  one  fourth  of . 

Six  is of  twelve. 


Nine  is 


of  twelve. 


7.  Three  times  2  are 

8.  Three  times  4  are 

9.  Four  times  3  are  - 

10.  Two  times  6  are  - 

11.  Two  times  4  are  - 

12.  Two  times  2  are  - 


2  is  i  of  - 

4  is  ^  of  - 
6  is  ^  of  - 

3  is  I  of  - 

5  is  i  of  - 
8  is  I  of  - 

3  times  3 

4  times  2 

6  times  2 
2  times  5 
2  times  3 

5  times  2 


FOR    DRILL    IN    ADDING. 


5 

5 


4 
2 


8 

2 


2 

3 

4 

8 

9 

2 

5 

5 

1 

2 

3 

1 

3 

2 

1 

2 

8 

6 

6 

3 

5 

5 

6 

4 

4 

4 

2 

3 

4 

3 

3 

1 

4 

8 

9 

7 

7 

9 

7 

1 

4 

3 

2 

4 

3 

1 

2 

1 

(1)  Eead,  and  give  differences.     (2)  Copy  and  subtract. 

20     30     40     50     60     70 
14     14     14     15     15     15 


PART  I.  33 

1.  Imagine  12  marks  on  the  blackboard;  then 
imagine  that  you  erase  half  of  them ;  then  imagine 
that  you  erase  one  half  of  the  remainder.  How 
many  marks  do  you  now  seem  to  see  upon  the 
blackboard  ? 

2.  Imagine  a  4-inch  square  drawn  upon  the 
blackboard ;  imagine  it  divided  into  equal  parts  by 
a  vertical  line ;  also  imagine  a  horizontal  line  that 
would  divide  the  square  into  two  equal  parts.  Into 
how  many  equal  parts  does  the  square  now  seem 
to  be  divided?  Each  part  is  what  kind  of  a 
square?  How  many  2-inch  squares  in  a  4-inch 
square  ? 

3.  Imagine  a  1-inch  square  drawn  upon  your 
slate.  It  has  how  many  sides?  Each  side  is  how 
long?     How  far  is  it  around  a  1-inch  square? 

4.  Imagine  a  2 -inch  square  drawn  upon  the 
blackboard.  It  has  how  many  sides?  Each  side 
is  how  long  ?     How  far  is  it  around  a  2-inch  square? 

5.  Imagine    a    3-incli    square    drawn   upon   the 

blackboard.     It  has sides.     Each  side  is 

inches  long.    How  far  is  it  around  a  3-inch  square  ? 

6.  How  far  is  it  around  a  4-inch  square? 

(1)  Eead,  and  give  products.     (2)  Copy  and  multiply. 

20  21  22  20  30  31 

4  4  4  5  4  4 


34  ELEMENTAKY   ARITHMETIC. 

1.  Imagine  that  you  have  a  stick  of  candy  1 
foot  long;  imagine  that  you  give  one  third  of  it  to 
your  brother;  imagine  that  you  break  the  remain- 
der into  two  equal  pieces.  How  many  inches  long 
is  each  piece? 

2.  Imagine  an  oblong  bounded  by  two  vertical 
lines  each  1  inch  long,  and  two  horizontal  lines 
each  3  inches  long.  How  many  such  oblongs 
would  be  equal  to  a  3-inch  square? 

3.  Imagine  four  1-inch  squares  cut  from  paper. 
So  arrange  them  that  they  together  will  make  a 
square.     What  kind  of  a  square  is  it? 

4.  Imagine  nine  1-inch  squares  cut  from  paper. 
So  arrange  them  that  they  together  will  make  a 
square.     What  kind  of  a  square  is  it? 

5.  Imagine  an  oblong  1  inch  wide  and  3  inches 
long.  Imagine  this  oblong  divided  into  1-inch 
squares.  How  many  1-incli  squares  do  you  seem 
to  see? 

6.  Imagine  eight  1-inch  squares  cut  from  paper. 
So  arrange  them  that  they  together  will  make  an 
oblong  2  inches  wide.     How  long  is  the  oblong? 

7.  How  many  inches  around  an  oblong  4  inches 
long  and  2  inches  wide? 

(1)  Read,  and  give  quotients.     (2)  Copy  and  divide. 

3^)60^       3^)66^       3^)69^       4^)80^       4^)88^ 


PART  I. 


35 


1.  In  one  whole  there  are 

2.  In  one  whole  there  are 

3.  In  one  half  there  are  - 


-  halves. 

-  fourths, 
fourths. 

fourths. 


fourth. 


4.  One  half  and  1  fourth  are 

5.  One  half  less  1  fourth  is  — 

6.  One  half  of  one  half  is  one 


7.  Jane  ate  one  half  of  a  j^ie;  Harold  ate  one 
fourth  of  a  pie;  together  they  ate  of  a  pie. 

8.  Webb  had  one  half  of  a  pie;  he  gave  one 

fourth  of  a  pie  to  his  sister ;  he  then  had 

of  a  pie. 

9 .  Robert  had  one  fourth  of  a  pie ;  Arthur  had 

three  times  as  much;  Arthur  had  of 

a  pie. 

10.  Mrs.  Johnson  divided  a  pie  equally  among 
some  children,  giving  to  each  child  one  fourth  of  a 
pie;  there  were  children. 

11.  Mrs.  Clark  divided  one  half  of  a  pie  equally 

between  two  children;    each  child  received  

of  a  pie. 

(1)  Read,  and  give  quotients.      (2)  Copy  and  divide. 

2)60^         3)60^         4)80^         2)84^         4)84^ 


36  ELEMENTARY    ARITHMETIC. 


I         I         I.I 


1.  One  inch  is  half-inches. 

2.  One  inch  is  fourth-inches. 

3.  One  half -inch  is  fourth  inches. 

4.  Two  half -inches  are  inch. 

5.  Four  fourth-inches  are  inch. 

6.  Two  fourth-inches  are of  an  inch. 

7 .  One  half -inch  and  1   fourth-inch .  are  

fourth-inches. 

8.  One  half -inch  less  1  fourth-inch  is  . 

9.  Two  times  1  fourth-inch  are  fourth- 
inches,  or  half -inch. 

10.  One  fourth-inch  is  contained  in  one  half- 
inch  times. 

11.  Alice's  pencil  is  two  and  one  half  inches 
long;  Jane's  pencil  is  two  and  one  fourth  inches 

long;   together  they  are 

inches  long. 

12.  Sarah's  pencil  is  two  and  one  fourth  inches 
long;  Mary's  is  three  times  as  long;  Mary's  pencil 
is ■ inches  long. 

13.  Laura  had  a  pencil  two  and  one  half  inches 
long ;  she  broke  it  into  pieces,  each  piece  being  one 
half -inch  long;  there  were  pieces. 

(1)  Bead,  and  give  sums.     (2)  Copy  and  add. 
2  fourths  2|  23|  3|  24| 

1  fourth  2|  10|  Si  104- 


PART    I. 


37 


1.  One  dollar  is  equal  in  value  to  half- 
dollars. 

2 .  One  dollar  is  equal  in  value  to  fourth- 
dollars. 

3.  One  half-dollar  is  equal  in  value  to  

fourth-dollars.     A  fourth-dollar  is  sometimes  called 
a  "  quarter,"  or  a  quarter  of  a  dollar. 

4.  One  half  of  a  dollar  and  one  fourth  of  a 
dollar  are  — fourths  of  a  dollar. 

5.  One  half   of   a  dollar  less  one  fourth  of  a 
dollar  is of  a  dollar. 

6.  Four  times   one   fourth  of   a   dollar  equals 
fourths  of  a  dollar,  or  dollar. 


7.  One  fourth  of  a  dollar  is  contained  in  one 
half  of  a  dollar  times. 

8.  One  half  of  one  half  of  a  dollar  is  

of  a  dollar. 


(1)  Read,  and  give  differences.      (2)  Copy  and  subtract. 

3  fourths  3f  25f  8i  27i 

1  fourth  li  lOi  5i  lOi 


38  ELEMENTARY    ARITHMETIC. 

1.  One  half  of  a  foot  and  one  fourth  of  a  foot 
are  inches. 

2.  One  half  of  a  dollar  and  one  fourth  of  a  dol- 
lar are  cents. 

3.  One  half  of  a  pie  and  one  fourth  of  a  pie  are 
fourths  of  a  pie. 

4.  One  half  of  an  inch  and  one  fourth  of  an  inch 
are  fourths  of  an  inch. 

5.  One  half  of  a  square  inch  and  one  fourth  of 
a  square  inch  are  fourths  of  a  square  inch. 

6.  Fred  bought  a  knife;  the  price  was  half  a 
dollar;  he  gave  the  salesman  one  dollar;  Fred 
should  receive  in  change  . 

7.  At  a  quarter  of  a  dollar  a  pound,  4  pounds  of 
coifee  cost  . 

8.  I  paid  half  a  dollar  for  butter  at  one  fourth 
of  a  dollar  a  pound;  I  bought  pounds. 

9.  Bessie  had  a  pencil  two  and  one  half  inches 
long ;  she  broke  it  into  two  equal  parts ;  each  part 
was  inches  long. 

10.  One  half  of  2^  inches  is  . 

Acid.  Subtract.  Multiply.  Divide. 

1  fourth        3  fourths        2  fourths        2)4  fourths 
3  fourths       1  fourth  2 


(1)  Read,  and  give  products.     (2)  Copy  and  multiply. 

3  fourths  5i  23i  3i  23i 

2  2  •  2  2  2 


PART  I. 


39 


1.  There  are  seven  clays  in  a  tveek. 

2.  Eight  days  are  1  week  and  day. 

3.  Nine  days  are  1  week  and  days. 

4.  Twelve  days  are  1  week  and  days. 

5.  Eleven  days  are  1  week  and  days. 

6.  Ten  days  are  1  week  and  days. 


7.  One  w^eek  and  2  days  are 

8.  One  week  and  5  days  are 

9.  One  week  and  3  days  are 

10.  One  week  and  4  days  are 

11.  One  dime  and  1  cent  are 


days, 
days, 
days, 
days. 

cents. 
—  cents. 


12.  Twelve  cents  and  1  dime  are  — 

13.  Two  dimes  are  cents.     3  dimes  = 

14.  Six  dimes  are  cents.     4  dimes  = 

15.  Two  dimes  and  2  cents  are  cents. 


16.  Two  dimes  and  5  cents  are 


cents. 


17.  Two  quarts  and  1  pint  are  j)ints. 

18.  Four  quarts  and  1  pint  are  pints. 

19.  Five  pints  are  quarts  and  1  pint. 

20.  Nine  pints  are  quarts  and  1  pint. 


21.  Two  yards  and  1  foot  are 

22.  Two  yards  and  2  feet  are 


feet, 
feet. 


(1)  Eead,  and  give  quotients.     (2)  Copy  and  divide. 

3  ft.)36  ft.     2ft.)24ft.     4ft.)48ft.     5  ft.) 25  ft. 
—  times 


40  ELEMENTARY   ARITHMETIC. 

1.  If  Harry  steps  2  feet  at  each  step,  how 
many  steps  will  he  take  in  walking  12  feet?  20 
feet?     40  feet?     100  feet? 

2.  If  Mary  steps  H  feet  at  each  step,  how 
many  steps  will  she  take  in  walking  3  feet?  6 
feet?     9  feet?     12  feet? 

3.  If  Harry's  father  steps  2^  feet  at  each  step, 
how  many  steps  will  he  take  in  walking  5  feet? 
10  feet?     15  feet?     20  feet? 

4.  One  half  of  seven  feet  is  feet. 

5.  One  half  of  nine  feet  is  —  feet. 

6.  One  half  of  eleven  feet  is  feet. 

7.  One  third  of  six  feet  is feet. 

8.  One  third  of  seven  feet  is  — — ■  feet. 

9.  One  third  of  nine  feet  is  feet. 

10.  One  third  of  ten  feet  is — —  feet. 

(1)  Read,  and  give  quotients.     (2)  Copy  and  divide. 
2)24  feet        2)25  feet        2)26  feet        2)27  feet 

2)44  feet        2)45  feet        2)46  feet        2)47  feet 


PART    II. 

9  8  7 

4  5  6 

13  13  13 

1.  Nine  and  4  are  .  8  and  4  are 

2.  Seven  and  5  are  .  8  and  5  are 

3.  Nine  and  3  are  .  6  and  5  are 

4.  Seven  and  6  are  .  7  and  4  are 

5.  Thirteen  less  9  are  .    13  less  7  are 

6.  Thirteen  less  8  are .    13  less  4  are 

7.  Thirteen  less  6  are  .    13  less  5  are 

8.  Twelve  units,  or  ones,  make  one  dozen. 

9.  Thirteen  is  one  dozen  and  . 

10.  Thirteen  inches  are  1  foot  and  . 


11.  Thirteen  cents  are  1  dime  and cents. 

12.  Thirteen  days  are  one  week  and  ■ days. 

13.  Thirteen  pints  are  6  quarts  and  pint. 

14.  Thirteen  feet  are  4  yards  and  foot. 


Copy  and  add: 

25     26 

27 

28 

26 

28 

25     26 

25 

23 

24 

24 

41 


42  ELEMENTARY   ARITHMETIC. 

1.  Seven  quarts  of  milk  and  6  quarts  of  milk 
are  quarts  of  milk. 

2.  Eight   pounds  of    sugar  and    4    pounds  of 
sugar  are  pounds  of  sugar. 

3.  Twelve    loads   of   gravel    less    7    loads   of 
gravel  are  loads  of  gravel. 

4.  Thirteen   pairs   of   horses   less    6    pairs   of 
horses  are  pairs  of  horses. 

5.  Three  times  4  books  are  books. 

6.  Two  times  6  birds  are birds. 

7.  Three   inches   are   contained   in  12  inches 

times. 

8.  Three   inches   are   contained   in  13  inches 

times  with  one  inch  remainder. 


9.  One  third  of  12  inches  is inches. 

10.  One  third  of  13  inches  is  . 

11.  Four  inches  are  contained  in  12  inches 

times. 

12.  Four  inches  are  contained  in  13  inches 

times  with  inch  remainder. 

13.  One  fourth  of  12  inches  is  inches. 

14.  One  fourth  of  13  inches  is  . 

15.  Five  inches  are  contained  in  10  inches . 

16.  Five  inches  are  contained  in  13  inches  

times  with  inches  remainder. 

Copy  and  subtract: 

42     52     62     72     82     92 
16      16      16      16     16      16 


PART    II.  43 


■D 


1.  The  line  A  B  is long. 

2.  The  line  C  D  is  inches  long. 

3.  How  many  inches  longer  is  C  D  than  A  B? 
C  D  is  inches  longer  than  A  B. 

4.  A  B  and  C  D  together  are inches  long. 

5.  C  D  is  how  many  times  as  long  as  A  B? 
C  D  is  times  as  long  as  A  B. 

6.  A  B  is  equal  to  what  part  of  C  D?     A  B  is 
equal  to of  C  D. 


7.  The  sum  of  8  and  5  is  . 

8.  The  difference  of  8  and  5  is  . 

9.  The  product  of  40  and  2  is  . 

10.  The  quotient  of  8  divided  by  2  is  -. 

11.  The  sum  of  two  numbers  is  13;    one  of  the 
numbers  is  9 ;  the  other  number  is  . 

12.  The  difference  of  two  numbers   is  5;    the 
greater  number  is  13;  the  less  number  is  . 

13.  The  difference  of  two  numbers  is  4;    the 
less  number  is  9 ;  the  greater  number  is . 

Copy  and  multiply : 

26  36  46  25  24  15 

2  2  2  3  3  3 


44  ELEMENTARY    ARITHMETIC. 

1.  Mary  had  13  canaries;  slie  sold  8  of  them; 
she  then  had  canaries. 

2 .  Henry  lives  9  miles  north  of  Aurora ;  James 
lives  4  miles  south  of  Aurora ;  from  Henry's  home 
to  James's  home  it  is  miles. 

3.  William  had  13  cents;  he  bought  two  or- 
anges at  5  cents  each;   he  then  had  cents. 

4.  A  ton  of  coal  cost  6  dollars;  a  cord  of  wood 

cost  4  dollars;    the  coal  cost  dollars  more 

than  the  wood;  the  wood  and  coal  together  cost 
dollars. 

5.  Robert  is  8  years  old,  and  his  sister  is  5 

years  older  than  he  is;    Robert's  sister  is  

years  old. 

6.  John  gathered  13  roses  and  gave  6  of  them 
to  his  sister;  he  kept  roses. 

7.  One  fourth  of  8  inches  is  inches. 

8.  One  fourth  of  9  inches  is  inches. 

9.  One  half  of  13  inches  is  . 

10.  If  one  barrel  of  apples  costs  $2 J,  two  bar- 
rels cost    ;    three  barrels  cost    ;    four 

barrels  cost  . 

11.  If  one  ton  of  coal  is  worth  $6-|^,  two  tons 
are  worth . 

12.  If  one  cord  of  wood  is  worth   $4^,  two 
cords  are  worth  . 

Copy  and  divide : 

$2)$30     $2)$50     $2)$70   .  $2)$90 


PART  II. 


45 


IS 


1.  One  whole  is 

2.  One  whole  is 


fourths. 

sixths. 


3.  One  half  is  how  many  fourths? 
fourths. 


One  half 


4.  One  half  is  how  many  sixths?     One  half  is 
—  sixths. 

5.  One  half  and  one  fourth  are  fourths. 

6.  One  half  and  one  sixth  are  sixths. 


7.  One  half  less  one  fourth  is 

8.  One  half  less  one  sixth  are 

9.  One  half  less  two  sixths  is 

10.  Two  times  one  fourth  are  - 

11.  Two  times  one  sixth  are  — 

12.  Two  times  two  sixths  are  - 


13.  Three  times  two  sixths  are  

14.  One  fourth  is  contained  in  1  half 

15.  One  sixth  is  contained  in  1  half 

16.  One  half  of  one  half  is  — 

17.  One  third  of  one  half  is 


—  fourth. 

—  sixths. 

—  sixth. 

—  fourths, 
sixths. 

—  sixths. 

—  sixths. 


times, 
times. 


Copy  and  divide : 

2)|30  2)$50 

—  dollars 


2)$70 


2)$90 


46  ELEMENTARY    ARITHMETIC. 


1.  One  half  of  a  pie  and  one  fourth  of  a  pie 
are  fourths  of  a  pie. 

2.  One  half  of  a  pie  and  one  sixth  of  a  pie  are 

sixths  of  a  pie. 

3.  One  half  of  a  pie  less  one  fourth  of  a  pie  is 

fourth  of  a  pie. 

4.  One  half  of  a  pie  less  one  sixth  of  a  pie  are 

sixths  of  a  pie. 

5.  Three  times  2  sixths  of  a  pie  are  . 


6.  Two  sixths  of  a  pie  are  contained  in  one 
whole  pie  times. 

7.  One  third  of  one  half  of  a  pie  is  . 

8.  Webb  had  one  half  of  a  pie;    he  gave  one 

sixth  of  a  pie  to  his   sister;    he  then  had  

of  a  pie. 

9.  Mrs.  Johnson  divided  a  pie  equally  among 
some  children,  giving  to  each  child  one  sixth  of  a 
pie;  there  were  children. 

10.  Mrs.  Clark  divided  one  half  of  a  j)ie  equally 
among  three  children;    each  child  received 


oi  a  pie. 

Copy  and  add: 

125      127 

126 

129 

128 

15      16 

14 

11 

14 

l^ART  11. 


47 


1  pint. 


1  quart. 


1  gallon. 


1.  Four  quarts  are  one  gallon. 

2.  Eight  quarts  are  gallons. 

3.  Twelve  quarts  are  gallons. 

4.  Two  gallons  are  quarts. 

6.  Two  quarts  are of  a  gallon. 

6.  Three  quarts  are  of  a  gallon. 

crallons, 

^—  o"allons. 
gal- 


7.  Five  quarts  are 

8.  Six  quarts  are 


and 
and 


9.  Seven  quarts  are  and 


Ions. 


costs 


10.  At  5  cents  a  quart,  one  half -gallon  of  milk 


cents. 


11.  At  12  cents  a  gallon,  two  quarts  of  milk 
cost  cents. 


Copy  and  subtract: 

140              140 

140 

130 

130 

15                16 

17 

18 

19 

48  ELEMENTARY    ARITHMETIC. 

1.  One  quart  and  one  pint  are  pints. 

2.  One  gallon  and  one  quart  are  quarts « 

3.  One  foot  and  one  inch  are  inches. 

4.  One  yard  and  one  foot  are feet. 

5.  One  dime  and  one  cent  are  cents. 

6.  One  half  and  one  fourth  are fourths. 

7.  One  half  and  one  sixth  are  sixths. 

8.  One  nickel  and  one  cent  are  cents. 

9.  At  40  cents  a  gallon,  two  quarts  of  syrup 
cost  cents. 

10.  At  20  cents  a  quart,  one  half -gallon  of  lard 
oil  costs  cents. 

11.  At  12  cents  a  gallon,  one  quart  of  kerosene 
costs  cents. 

12.  At  2  cents  a  quart,  one  gallon  of  skimmed 
milk  costs  cents. 

13.  Will  Blake  carried  to  Mr.  Jones  a  pint  of 
milk  each  day  for  two  weeks;    in  all  he  carried 

pints,   or    quarts,   or  one   gallon  and 

quarts. 

14.  Mrs.  Bean  buys  two  quarts  of  milk  each 
day,  for  which  she  pays  5  cents  a  quart ;  each  day 

the  milk  costs  cents;  for  one  week  the  milk 

costs  cents. 


Copy  and  multiply : 

126              136 

146 

125 

124 

2                  2 

2 

3 

3 

PART    II.  49 

.  1.  Nine  books  and  4  books  are  books. 

2.  Six  apples  and  five  apples  are  apples. 

3.  My  book  is  inches  wide. 

4.  If  I  slioiild  draw  an  oblong  3  inches  wide 
and  4  inches  long,  and  then  divide  it  into  1-inch 

squares,  there  would  be  rows  of  squares,  and 

in  each  row  there  would  be  squares.     An 

oblong  3  inches  by  4  inches  contains  ■ square 

inches. 

5.  Three  times  4  square  inches  are  . 

6.  Four  times  3  square  inches  are  . 

7.  Jane  had  a  piece  of  ribbon  13  inches  long; 
she  cut  from  it  pieces  3  inches  long;  when  she 
had  cut  off  4  pieces,  she  had left. 

8.  Byron  pays  2  cents  each  for  oranges,  and 
sells  them  for  4  cents  each;  on  1  orange  he  gains 
cents ;  on  6  oranges  he  gains  cents. 

9.  Harry  pays  10  cents  a  dozen  for  eggs  and 
sells  them  at  13  cents  a  dozen;  on  1  dozen  he 
gains cents;  on  4  dozen  he  gains cents. 

10.  Ten  days  are  one  week  and  days. 

11.  To-day  is  Monday.    Seven  days  from  to-day 
will  be  .      Eight  days  from  to-day  will  be 


12.  An  old  hen  sat  upon  13  eggs;  all  the  eggs 
hatched  except  4 ;  there  were  chickens. 

Copy  and  divide : 

$2)$32     $2)$52     $2)$72     $2)$92 


50  ELEMENTARY    ARITHMETIC. 

1.  Howard  has  a  string  2  and  1  half  feet  long; 
David  has  a  string  2  and  1  fourth  feet  long;  to- 
gether the  strings  are  and  fourths  feet 

long. 

2.  Draw  an  oblong  2  and  1  half  inches  wide; 
make  it  twice  as  long  as  it  is  wide ;  it  will  be 


inches  long. 

3.  The  teacher  bought  2  and  1  half  yards  of 
ribbon;  she  cut  it  into  pieces  1  fourth  of  a  yard 
long ;  there  were  pieces. 

4.  Mary  had  a  stick  of  molasses  candy  1  and  1 
half  feet  long ;  she  cut  it  into  pieces  1  sixth  of  a 
foot  long;  there  were  pieces. 

5.  One  half  of  2  and  1  half  inches  is . 

6.  One  third  of  6  and  1  half  inches  is . 

7.  Ellen  had  a  piece  of  ribbon  1  half  of  a  yard 
long;  Sarah  had  a  piece  1  sixth  of  a  yard  long; 
together  they  had of  a  yard. 

8.  Emma  lives  1  half  of  a  mile  north  of  the 
schoolhouse;  Eva  lives  one  fourth  of  a  mile  south 
of  the  schoolhouse;  from  Emma's  home  to  Eva's 
home  it  is of  a  mile. 

9.  The  cyclometer  on  Willie's  bicycle  showed 
that  he  had  ridden  10  and  1  half  miles;   James 

had  ridden  twice  as  far;   James  had  ridden  

miles. 

Copy  and  divide: 

2)$32  2)$52  2)$72  2)$92 


14 


PART  II. 

9 
5 

8 
6 

7 

7             7  twos  are  14 

— 

2  sevens  are  14 

14 


51 


14 


1.  Nine  and  5  are  - 

2.  Seven  and  6  are 

3.  Seven  and  5  are 


4.  Fourteen 

5.  Fourteen 

6.  Fourteen 

7.  Fourteen 

8.  Fourteen 

9.  14  is  — 


10.  Fourteen 

11.  Fourteen 

12.  Fourteen 

13.  Fourteen 

14.  Fourteen 

15.  Fourteen 

16.  Foin^teen 

17.  Fourteen 
quarts. 

18.  Fourteen 

19.  Fourteen 

20.  Fourteen 

Copy  and  add : 

135  132 

25  28 


less  9  are  . 

less  5  are  . 

less  6  are  . 

less  12  are  . 

less  4  are  . 

-  7's.     14  is  — 
is  one  dozen  and 


8  and  5  are  

7  and  7  are  

8  and  6  are  

14  less    7  = 

14  less    8  = 

14  less  10  = 

-.     14  less  11  = 


14  less 
2's. 


inches  are  1  foot  and  — 
cents  are  1  dime  and  - 

days  are  weeks. 

pints  are  quarts. 

pints. 


2  = 


inches, 
cents. 


quarts  are  — 

feet  are  3  yards  and  feet. 

quarts   are    3   gallons   and 


eggs  are  1  dozen  and  — 
cents  are  2  nickels  and  - 
sixths  are  2  wholes  and 


eggs. 
-  cents. 


134 
36 


137 
25 


136 

26 


52  ELEMENTARY    ARITHMETIC. 

1.  Eight  gallons  of  milk  and  6  gallons  of  milk 
are  — — -  gallons  of  milk. 

2.  Nine  pairs  of  ponies  and  4  pairs  of  ponies 
are  pairs  of  ponies. 

3.  Fourteen  loads  of  hay  less  9  loads  of  hay 
are  loads  of  hay. 

4.  Fourteen  boxes  of  berries  less  8  boxes  of 
berries  are  boxes  of  berries. 

5.  Two  times  7  marbles  are  marbles. 

6.  Seven  times  2  horses  are  horses. 

7.  7  inches  are  contained  in  14  inches  . 

8.  2  inches  are  contained  in  14  inches  . 

9.  6  inches  are  contained  in  14  inches  

times  with  a  remainder  of  inches. 

10.  5  inches  are  contained  in  14  inches  

times  with  a  remainder  of  inches. 

11.  4  inches  are  contained  in  14  inches  

times  with  a  remainder  of  inches. 

12.  3  inches  are  contained  in  14  inches  

times  with  a  remainder  of  inches. 

13.  One  half  of  14  inches  is  inches. 

14.  One   seventh   of   fourteen   inches   is    

inches. 

15.  Three  sevenths  of  14  inches  are inches. 

16.  Two  sevenths  of  14  inches  are  inches. 

17.  Five  sevenths  of  14  inches  are inches. 

Copy  and  subtract: 

150      150      150      150      150 
25      27      24      28       23 


PART  II. 


53 


1  in. 


.2         Ftg.  1. 


1.  The  jwrwietei'   of   a  figure   is   the   distance 
around  it. 

2.  The  perimeter  of  a  1-incli  square  is  

inches. 

3.  The  perimeter  of  a  2-inch  square  is  

inches. 

4.  The  perimeter  of  a  3-inch  square  is  

inches. 

5.  The  perimeter  of  Fig.  2,  at  the  beginning  of 
this  page,  is  inches. 

6.  The  sum  of  9  and  5  is  . 

7.  The  difference  of  14  and  9  is . 

8.  The  product  of  7  and  2  is  . 

9.  The  quotient  of  140  divided  by  2  is  . 

10.  The  sum  of  two  numbers  is  14;  one  of  the 
numbers  is  8 ;  the  other  number  is  . 


1 1 .  The  difference  of  two  numbers  is  4 ;  the  less 
number  is  10  ;  the  greater  number  is  . 


12.  The    difference  of  two  numbers  is   5 ;   the 
greater  number  is  14  ;  the  less  number  is  . 

Copy  and  multipl}^ : 

127  137  147  227 

2  2  2  2 


237 


54  ELEMENTARY    ARITHMETIC. 

1.  A  hen  had  14  chickens;  a  hawk  killed  6  of 
them;  she  then  had  chickens. 

2.  Peter   lives   5  miles   west  of   Anrora;    his 
cousin  lives  14  miles  west  of  Aurora;  from  Peter's 

home  to  his  cousin's  it  is  miles.     Peter  lives 

of  his  cousin. 

3.  At  7  cents  each,  2  melons  cost  cents. 

4.  Charles  pays  3  cents  a  bag  for  pop-corn  and 

sells  it  at  5  cents  a  bag ;  on  one  bag  he  gains 

cents;  on  three  bags  he  gains  cents. 

5.  When  oranges  cost  2  cents  each,  for  14  cents 
I  can  buy  oranges. 

6.  Willie  paid  70  cents  each  for  two  books; 
for  both  he  paid  . 

7.  I  paid  1  dollar  and  20  cents  (120^)  for  2 
yards  of  lace;  one  yard  cost  cents. 

8.  One  fifth  of  10  inches  is  inches. 

9.  One  fifth  of  11  inches  is  inches. 

10.  One  fifth  of  12  inches  is  inches. 

11.  If  one  barrel  of  flour  costs  $3^,  two  barrels 

cost  ;  three  barrels  cost  ;    four  barrels 

cost  . 

12.  If  one  ton  of  coal  is  worth  $6^,  two  tons 
are  worth  . 

13.  Two  times  5^  are  .     2  times  5J  = 

Copy  and  divide: 

2^)34^  2^)54^  2^)74^  2^)94^ 

—  times 


PART  II. 


55 


1.  One  whole  is 

2.  One  half  is  - 


3.  One  fourth  is 


—  eighths. 

—  eighths. 

—  eighths. 

4.  Three  fourths  are  eighths. 

5.  One  half  and  one  eighth  are  — — 

6.  One  fourth  and  one  eighth  are  — 

7.  One  half  and  two  eighths  are  — 

8.  One  fourth  and  two  eighths  are  — 

9.  One  half  and  three  eighths  are  — 

10.  One  half  less  one  eighth  are  

11.  One  fourth  less  one  eighth  is  - — - 

12.  One  half  less  three  eighths  is  — 


eighths. 

-  eighths, 
eighths. 

-  eighths. 

-  eighths. 


eighths. 

eighth. 

-  eighth. 


13.  Two  times  one  eighth  are  eighths. 

14.  Two  times  two  eighths  are  eighths. 

15.  Two  times  three  eighths  are  eighths. 

16.  One  eighth  is  contained  in  one   half  

times. 

17.  One    eighth    is    contained    in    one    fourth 
times. 


18.  One  half  of  one  fourth  is 


eighth. 


Copy  and  divide: 

2)34^  2)54^ 


2)74^ 


2)94^ 


56  ELEMENTARY    ARITHMETIC. 


1.  One  half  of  an  inch  and  one  eighth  of  an 
inch  are  eighths  of  an  inch. 

2.  One  fourth  of  an  inch  and  one  eighth  of  an 
inch  are  eighths  of  an  inch. 

3.  One  inch  less  one  eighth  of  an  inch  are 
eighths  of  an  inch. 

4.  One  half  of  an  inch  less  one  eighth  of  an 
inch  are  eighths  of  an  inch. 

5.  One  fourth  of  an  inch  less  one  eighth  of  an 
inch  is  eighth  of  an  inch. 

6.  Three  times  three  eighths  of  an  inch  are 


7.  Two   times    five    eighths   of    an   inch   are 


8.  Four  times   three  eighths  of   an  inch  are 


9.  Three  eighths  of  an  inch  are  contained  in 
one  and  one  eighth  inches  (9  eighths) times. 

10.  Three  eighths  of  an  inch  are  contained  in 
one  and  one  half  inches  times. 

11.  Johnnie  had  a  S23linter  in  his  finger  one 
fourth  of  an  inch  long.  In  getting  it  out  his 
mother  broke  it  into  two  equal  pieces.  Each  piece 
was of  an  inch  long.     Johnnie  cried. 


Copy  and  add: 

230      250 

240 

220 

221 

120      132 

128 

136 

131 

PART  II. 


57 


1. 

2. 
pecks. 

3 

4. 

5. 

6. 

7. 

8. 

9. 
10. 
11. 
12. 
13. 
14. 
15. 


1  peck. 

Eight  quarts  are  one  jpeck. 
Twelve    quarts   are  


and 


Four  jpeeks  are  one  husliel. 


Eight  pecks  are  - 
Twelve  pecks  are 
One  quart  is 


Three  quarts  are 
Five  quarts  are  - 
Seven  quarts  are 
One  peck  is  


bushels. 

-  bushels. 

-  of  a  peck. 

of  a  peck. 

of  a  peck. 

of  a  peck. 


Two  pecks  are  - 
Three  pecks  are 
Five  pecks  are  - 
Two  bushels  are 


of  a  bushel. 

—  of  a  bushel. 

of  a  bushel. 


—  pecks. 
One  bushel  and  3  pecks  are  pecks. 


Copy  and  subtract: 

270      206      309 
120      104      105 


425 
102 


536 
124 


58 


ELEMENTARY    ARITHMETIC. 


1.  Two 

2.  Two 

3.  Two 

4.  Two 

5.  Two 

6.  Two 

7.  Two 

8.  Two 

9.  Two 

10.  Two 

11.  Two 

12.  Two 
eighths. 


quarts  and  one  pmt  are  - 
gallons  and  one  quart  are 
feet  and  one  inch  are  - — 


pints. 
-  quarts. 


yards  and  one  foot  are  — 
dimes  and  one  cent  are  — 
pecks  and  one  quart  are  - 
bushels  and  one  peck  are  - 
nickels  and  one  cent  are  - 
halves  and  one  fourth  are  - 
halves  and  one  sixth  are  - 
halves  and  one  eighth  are  - 
fourths    and    one    eighth    are 


inches. 

—  feet. 

—  cents. 

—  quarts. 

—  pecks. 

—  cents. 

—  fourths. 

—  sixths. 


eighths. 


13.  How  many  of  the  class  can  read  the  first  12 
statements  on  this  page,  filling  each  blank  with 
the  right  number,  in  one  minute  or  less? 

14.  Can  you  read  the  first  eight  statements  on 
page  48  in  thirty  seconds  or  less?     Try  it. 

15.  At  20  cents  a  peck,  one  bushel  of  potatoes 
costs  cents. 

16.  At  10  cents  a  quart,  one  peck  of  beans  costs 
cents. 


17.  At  40  cents  a  bushel,  one  peck  of  apples 
costs  cents. 


Copy  and  multiply : 

206  207  205 

2  2  2 


215 

2 


216 

2 


PART  It.  59 

1.  Nine  slates  and  five  slates  are  slates. 

2.  Seven  dollars  and  six  dollars  are   . 

3.  My  book  is  inches  long. 

4.  If  I  should  draw  an  oblong  2  inches  wide 
a^nd  7  inches  long,  and  then  divide  it  into  1-inch 

squares,  there  would  be  rows  of  squares,  and 

in  each  row  there  would  be  squares.     An 

oblong  2  inches  by  7  inches  contains  square 

inches. 

5.  Two  times  7  square  inches  are  . 

6.  SeA'en  times  2  square  inches  are  . 

7.  Henry  is  5  feet  1  inch  tall;    his  sister  is 

4  feet  6  inches  tall;  Henry  is  inches  taller 

than  his  sister. 

8.  Jane  had  a  piece  of  red  ribbon  14  inches 
long;  she  cut  from  it  pieces  4  inches  long;  when 
she  had  cut  off  3  pieces,  she  had left. 

9.  In  14  there  are  fours  and  . 

10.  In  14  there  are  sixes  and  . 

1 1 .  Byron  buys  apples  at  1  half  a  cent  each  and 
sells  them  for  1  cent  each;  on  one  apple  he  gains 
;  on  14  apples  he  gains  cents. 

12.  Fourteen  days  are  weeks.     To-day  is 

Two   weeks   from   to-day   will   be 


Fifteen  days  from  to-day  will  be  .     Thirteen 

days  from  to-day  will  be  . 

Copy  and  divide: 
2  qt.)120  qt.  2  qt.)124  qt.  2  qt.)140  qt. 


60  ELEMENTARY    ARITHMETIC. 

1 .  Howard  has  two  pieces  of  board ; .  one  piece 
is  1  and  one  eighth  inches  thick ;  the  other  is  1  and 

one  fourth  inches  thick;   together  they  are 

and inches  thick. 

2.  Draw  an  oblong  2  and  three  eighths  inches 
wide;  make  it  twice  as  long  as  it  is  wide.  It  will 
be  and  ■ inches  long. 

3 .  Two  times  2  and  three  eighths  = 

4.  Draw  a  line  1  and  one  half  inches  long; 
divide  it  into  parts  each  one  eighth  of  an  inch 
long;  there  are  parts. 

5.  Two  eighths  of  an  inch  are  contained  in  1 
and  one  half  inches  (12  eighths) times. 

6.  One  half  of  4  and  one  fourth  is  — . 

7.  Harry  pays  12 J  cents  a  dozen  for  eggs;  he 
sells  them  at  15  cents  a  dozen;  on  one  dozen  he 
gains  ;  on  two  dozen  he  gains  cents. 

8.  In  14  there  are  threes  and  . 

9.  In  14  there  are  fives  and  . 

10.  One  seventh  of  14  cents  is  cents. 

11.  Two  sevenths  of  14  cents  are  cents. 

12.  Three  sevenths  of  14  cents  are  one  half  of 
cents. 

13.  Clyde  had  14  cents;  he  spent  4  sevenths  of 

his  money;    he   spent  cents   and  had  

cents  left. 

Copy  and  divide: 
2)120  qt.        2)124  qt.        2)140  qt.        2)144  qt. 


PART  11 

• 

61 

9             8 

g             7             3  fives  are  15 

5  threes  are  15 
15           15 

1. 

Nine  and  6  are  . 

8  and  6  are  — 

2. 

Nine  and  5  are  . 

8  and  7  are  — 

• 

3. 

Fifteen  less  9  are 

.    15  less  7  are 

4. 

Fifteen  less  8  are 

.    15  less  6  are 

. 

5. 

Fifteen  less  3  are 

.    15  less  10  are 

, 

6. 

Fifteen  less  4  are 

.    15  less  12  are 

• 

7. 

15  is  5's.     15  is 

5              3's. 

8. 

Fifteen  is  one  dozen  and  . 

9. 

Fifteen  inches  are  — 

—  foot  and  

-. 

10. 

Fifteen  cents  are 

•  dime  and 

cents. 

11. 

Fifteen  days  are  

weeks  and  — — 

-  day. 

12. 

Fifteen  pints  are 

quarts  and 

pint. 

13. 

Fifteen  quarts  are  — 

—  pints. 

14. 

Fifteen  feet  are  

vards. 

0 

15. 

Fifteen  quarts  are  — 

—  gallons  and  - 

— -. 

16. 

Fifteen  quarts  are  — 

—  peck  and  ■ — 

— . 

17. 

Fifteen  pecks  are  — 

—  bushels  and 

. 

18. 

Fifteen  halves  are  — 

—  wholes  and  - 

. 

19. 

Fifteen  thirds  are  

—  wholes. 

20. 

Fifteen  fourths  are  — 

— -  wholes  and 

• 

Copy  and  add: 

208 

206              209 

207 

208 

205 

107              206 

107 

207 

62  ELEMENTARY    ARITHMETIC. 

1.  Nine  bushels  of  potatoes  and  6  bushels  of 
potatoes  are  bushels  of  potatoes. 

2.  Eight  rows  of  trees  and  6  rows  of  trees  are 
rows  of  trees. 

3.  Fifteen  pounds  of  butter  less  7  pounds  of 
butter  are  pounds  of  butter. 

4.  Fifteen  quarts  of  walnuts  less  9  quarts  of 
walnuts  are  quarts  of  walnuts. 

5.  Three  times  5  lemons  are  lemons. 

6.  Five  times  3  oranges  are  oranges. 

7.  Five  quarts  are  contained  in  1  peck  and  7 
quarts  (15  quarts) times. 

8.  Three  quarts  are  contained  in  1  peck  and  4 
quarts  times. 

9.  One  half  of  15  inches  is  inches. 

10.  Fifteen  inches  are  one  half  of  inches. 

11.  One  third  of  15  inches  is  inches. 

12.  Two  thirds  of  15  inches  are  inches. 

13.  One  fifth  of  15  feet  is  feet. 

14.  Two  fifths  of  15  feet  are  feet. 

15.  Three  fifths  of  15  feet  are  feet. 

16.  Alice  had  15  apples;  she  gave  two  fifths  of 

them  to  her  sister ;  she  gave  her  sister apples 

and  had  apples  left. 

17.  Ten  balls  are  two  thirds  of  balls. 

Copy  and  subtract: 

215      214      213      215      215 
107      107      105      109      106 


PART  II. 


63 


lin. 


.2        Fig.  5. 


1.  A  triangle  has  sides. 

2.  An  oblong  has  sides. 

3.  A  pentagon  has  sides. 

4.  A  square  has  sides. 

5.  Figure  3  has  sides.     It  is  a 

6.  Figure  4  has  sides.     It  is  a 

7.  Figure  5  has  sides.     It  is  a 

8.  Figure  6  has  sides.     It  is  a 

9.  The  perimeter  of  figure  3  is  

10.  The  perimeter  of  figure  4  is  

11.  The  perimeter  of  figure  5  is  

12.  The  perimeter  of  figure  6  is  

Copy  and  multiply : 

205      204      215      214 
3       3       3       3 


inches, 
inches, 
inches, 
inches. 


225 
3 


64  ELEMENTARY    ARITHMETIC. 

1.  3  cents)  12  cents 

This  means,  find  lioiu  many  twies  S  cents  are 
contained  in  12  cents.  Three  cents  are  contained 
in  12  cents  times. 

2.  3)12  cents 

This  means,  find  one  third  of  12  cents.  One 
third  of  12  cents  is  cents. 

3.  3  cents)  15  cents 

This  means, r-. 

4.  3)15  cents 

This  means, . 

5.  James  lives  8  miles  north  of  the  Court 
House;  Joseph  lives  7  miles  south  of  the  Court 
House ;  from  James's  home  to  Joseph's  home  it  is 
miles. 

6.  At  night  the  out-door  temperature  was  9 
degrees  above  zero;  the  next  morning  it  was  6 
degrees  below  zero;  the  temperature  had  fallen 
— —  degrees.     What  was  the  season  of  the  year? 

7.  In  the  morning  the  out-door  temperature 
was  80  degrees  above  zero;  at  noon  it  was  90  de 

grees  above  zero;  the  temperature  had  risen  

degrees.     What  was  the  season  of  the  year? 

Copy  and  divide : 

3  ft.)120  ft.  3  ft.)126  ft.  5  ft.)150  ft. 


PAET  II. 


65 


One  whole  is 
One  half  is  - 


-  tenths, 
tenths. 


1. 

2. 
3. 

4. 

5.  One  half  and  three  tenths  are 

6.  One  half  and  two  tenths  are  - 


One  and  one  half  are  

One  half  and  one  tenth  are 


tenths. 


tenths. 

—  tenths. 

-  tenths. 


7.  One  half  less  one  tenth  are  

8.  One  whole  less  three  tenths  are 

9.  One  half  less  two  tenths  are  — 


tenths. 

—  tenths. 

-  tenths. 


10.  Two  times  three  tenths  are  tenths. 

11.  Four  times  two  tenths  are  tenths. 

12.  Three  times  four  tenths  are  . 

13.  Two  tenths  are  contained  in  six  tenths  — 

14.  Two  tenths  are  contained  in  one  whole  — 

15.  One  tenth  is  contained  in  one  half  . 


16.  One  fifth  of  one  half  is  — 

17.  One  fifth  of  one  whole  is 


tenths. 


18.  One  tenth  is  contained  in  two  wholes  . 

19.  One  half  is  contained  in  two  wholes  . 

Copy  and  divide : 

3)120  ft.        3)126  ft.         5)150  ft.         5)155  ft. 


66 


ELEMENTARY    ARITHMETIC. 


1.  One  dime  is  one  tenth  of  a  dollar. 

2.  One  half-dollar  is  tenths  of  a  dollar. 

3.  One  half  of   a  dollar  and  one  tenth  of   a 
dollar  are  tenths  of  a  dollar. 

4.  One  half  of  a  dollar  and  three  tenths  of  a 
dollar  are  tenths  of  a  dollar. 

5.  One  half  of  a   dollar  less  one  tenth  of  a 
dollar  are  tenths  of  a  dollar. 

6.  One  half  of  a  dollar  less  three  tenths  of  a 
dollar  are  tenths  of  a  dollar. 

7.  Three   times    three  tenths    of    a  dollar  are 
tenths  of  a  dollar. 


8.  Four  times  three  tenths  of  a  dollar  are 

tenths  dollars,  or  one  and  tenths  dollars. 

9.  Two  tenths  of  a  dollar  are  contained  in  one 
dollar  times. 

10.  One  tenth  of  a  dollar  is  contained  in  one 
half  of  a  dollar  times. 

1 1 .  One  fifth  of  one  Irnlf  of  a  dollar  is 

of  a  dollar. 


Copy  and  add: 

218      216 
105      107 

219 
106 

217 
107 

218 
107 

PART  II.  67 


1.  Can  you  add  column  (a)  in 
fifteen  seconds,  beginning  at  the  top  ? 

2.  Can  you  add  column  (a)  in 
fifteen  seconds,  beginning  at  the 
bottom  ? 

3.  Can  you  add  column  (b)  in 
fifteen  seconds? 

4.  Can  you  add  column  (c)  in 
fifteen  seconds? 

5.  Ten  twos  are  . 

6.  Fifteen  twos  are  . 

7.  Twenty  twos  are  . 


8.  Twenty-five  2's  are  — 

9.  Thirty  twos  are  

10.  Forty  twos  are  . 

11.  Fifty  twos  are  . 

12.  Two  fifties  are  . 

13.  Four  25's  are  . 

14.  One  fourth  of  100  is 

15.  One  fifth  of  100  is  — 

16.  75  is  three  fourths  of 

17.  40  is  two  fifths  of  — 


18.  Harry  had  one  dollar  (100 
cents);  he  spent  three  fourths  of  his 
money;  he  then  had  cents. 


a 

b 

c 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

1 

2 

2 

2 

2 

2 

1 

2 

2 

2 

2 

2 

2 

2 

2 

1 

2 

2 

1 

2 

1 

2 

2 

2 

1 

2 

2 

2 

2 

2 

2 

2 

2 

1 

2 

2 

2 

2 

2 

2 

2 

2 

1 

2 

2 

2 

2 

2 

1 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

1 

2 

1 

2 

1 

2 

2 

Copy  and  subtract : 

245              244 

243 

245 

245 

107              107 

105 

109 

106 

68  ELEMENTAEY    AKITHMETIC. 

1.  Three  quarts  and  1  pint  are  pints. 

2.  Three  gallons  and  1  quart  are  quartSo 

3.  Three  feet  and  1  inch  are  inches. 

4.  Three  yards  and  1  foot  are  feet. 

5.  Three  dimes  and  1  cent  are  cents. 

6.  Three  bushels  and  1  peck  are  pecks. 

7.  Three  nickels  and  1  cent  are  cents. 

8.  Three  halves  and  1  fourth  are fourths. 

9.  Three  halves  and  1  sixth  are  sixths. 

10.  There  were  100  trees  in  a  park;  one  fifth 
of  them  were  elms ;  one  fifth  were  maples,  and  the 
remainder   were   oaks.     There   were    elms, 

maples,  and  oaks. 

11.  There  were  100  people  at  a  banquet;  one 
fourth  of  them  were  men,  one  fourth  were  women, 
and  the    remainder   were    children.     There   were 

men, women,  and  children. 

12.  Sarah  bought  a  doll;  the  price  was  75  cents; 
she  gave .  the  salesman  one  dollar ;  she  should  re- 
ceive in  change  cents. 

13.  Howard  bought  seven  boxes  of  berries  at  10 
cents  a  box;  he  gave  the  salesman  one  dollar;  he 
should  receive  in  change  cents. 

14.  For  fifty  cents  I  can  buy   two-cent 

stamps. 

Copy  and  multiply : 

53  42  74  32  31  21 

3  3  2  4  5  6 


PART  II.  69 

1.  Nine  pens  and  six  pens  are  pens. 

2.  Eight  desks  and  seven  desks  are desks. 

3.  My  desk  is  inches  wide. 

4.  If  I  should  draw  an  oblong  3  inches  wide 
and  5  inches  long  and  then  divide  it  into  1  inch 

squares,  there  would  be  rows  of  squares,  and 

in  each  row  there  would  be  squares.     An 

oblong  3  inches  by  5  inches  contains  square 

inches. 

5.  Three  times  5  square  inches  are . 

6.  Five  times  3  square  inches  are  ■ . 

7.  Robert's  father  is  6  feet  2  inches  tall;  Rob- 
ert is  5  feet  1  inch  tall.  How  much  taller  is 
Robert's  father  than  Robert? 

8.  Alice  had  a  23iece  of  green  ribbon  15  inches 
long;    she   cut  from  it  pieces   four  inches   long; 

when  she  had  cut  off  3  pieces  she  had  inches 

left. 

9.  Byron  buys  peanuts  at  3  cents  a  bag;  he 
sells  them  at  5  cents  a  bag;  on  one  bag  he  gains 
• cents;  on  50  bags  he  gains  . 

10.  In  1  and  1  fourth  feet  there  are inches. 

11.  If  a  melon  costs  15  cents,  1  fifth  of  a  melon 
costs  • ■  cents. 

12.  If  I  drink  1  pint  of  milk  each  day,  in  2 
weeks  I  shall  drink  quarts  of  milk. 

Copy  and  divide : 

3^)42^  3^)72^  3^)45^  3^)75^ 


70  ELEMENTARY    ARITHMETIC. 

1.  Notice  that  tenths  may  be  written  in  more 
than  one  way : 

3  tenths         -^^  -3 

5  tenths         -^^  .5 

12  tenths         If         1.2 

1  and  2  tenths       1^-^         1-2 

2.  When  the  period  is  used  as  above  in  writing 
numbers,  it  is  called  a^;om^,  or  a  decimal  point. 

3.  Write  the  following  in  figures,  using  the 
decimal  point: 

4  tenths  1  and  4  tenths 

7  tenths  2  and  5  tenths 

9  tenths  3  and  8  tenths 

11  tenths  1  and  3  tenths 

15  tenths  2  and  1  tenth 

4.  Each  of  the  following  may  be  read  in  two 
ways: 

1.6  is  1  and  6  tenths,  or  16  tenths. 

1.3  is 

1.4  is  • 

2.5  is  ■ 

3.4  is — 

1.9  is —  

2.1  is  

3.5  is 

2.7  is  • — 

Copy  and  divide: 

3)42^  3)72^  3)45^  3)75^ 


PART  II. 


71 


9 

7 

16 


8 
8 

l6 


8  twos  are  16 
4  fours  are  16 


1.  Nine  and  7  are  - 

2.  Eight  and  8  are  ■ 

3.  Sixteen  less  7  are 

4.  Sixteen  less  8  are 

5 .  Sixteen  less  5  are 

6 .  Sixteen  less  4  are 


8  and  7  are  - 

9  and  6  are  — 


7.  16  is 


8's.     16  is 


16  less  9  are 
16  less  10  are 
16  less  12  are 
16  less  11  are 

— -  4's. 


8.  Sixteen 

9.  Sixteen 

10.  Sixteen 

11.  Sixteen 

12.  Sixteen 

13.  Sixteen 

14.  Sixteen 

15.  Sixteen 

16.  Sixteen 

17.  Sixteen 

18.  Sixteen 

19.  Sixteen 

20.  Sixteen 


is  one  dozen  and 


inches  are  - 
cents  are  — 
days  are  — 
pints  are  - 
quarts  are 
feet  are  — 


quarts  are 
quarts  are 
pecks  are  - 
tenths  are 
eio^hths  are 
fifths  are  - 


—  foot  and  — 
■  dime  and  - 
weeks  and 

—  quarts. 

—  pints, 
yards  and 

—  gallons. 
— -  pecks. 

—  bushels. 

—  and  


inches. 

-  cents. 

-  days. 


foot. 


wholes. 


and 


tenths. 


fifth. 


24  3 


Q1     5 


Copy  and  add: 

31.3 
23.5 


26.2 
22.4 


21.4 
43.3 


46.1 
12.2 


72  ELEMENTARY    ARITHMETIC. 

1.  Nine  sj)ans  of  horses  and  7  spans  of  horses 
are  spans  of  horses. 

2.  Eight  loads  of  coal  and  7  loads  of  coal  are 
loads  of  coal. 


3.  Sixteen  gallons  of  oil  less  9  gallons  of  oil 
are  gallons  of  oil. 

4.  Sixteen  pounds  of  cheese  less  8  pounds  of 
cheese  are  pounds  of  cheese. 

5.  Two  times  8  days  are  days. 

6.  Four  times  4  bushels  are  bushels. 

7.  Two  inches  are  contained  in  one  foot  and  4 
inches  (16  inches) times. 

8.  Four  inches  are  contained  in  1  foot  and  4 
inches  times. 

9.  Five  inches  are  contained  in  16  inches  

times  with  a  remainder  of  inch. 

10.  Six  inches  are  contained  in  16  inches  

times  with  a  remainder  of"  —  inches. 

11.  Seven   inches    are    contained   in    16   inches 
times  with  a  remainder  of  inches. 


12.  One  third  of  16  feet  is and  • 

feet. 

13.  Two  thirds  of  16  feet  are  . 

14.  One  eighth  of  16  feet  is  feet. 

15.  Three  eighths  of  16  feet  are  feet. 

Copy  and  subtract: 

363-V  48.4  66.8  35.5  73.7 

223-V  23.2  14.2  10.2  21.4 


PART  II. 

Fig.  7. 


73 


lin. 

d 

•r-( 
1—1 

lin. 

lin. 

d 

•  1-1 

1 .  By  the  area  of  a  figure  we  mean  the  amount 
of  its  surface.     The  area  of  Fig.  7  is sq.  in. 

2.  The  23erimeter  of  Fig.  7  is  inches. 

3.  The  perimeter  of  a  2-inch  square  is  

inches.    The  area  of  a  2-inch  square  is sq.  in. 

4.  The  perimeter  of  a  3-inch  square  is  

inches.    The  area  of  a  3-inch  square  is sq.  in. 

5.  The  area  of  a  4-inch  square  is sq.  in. 

6.  The  perimeter  of  an  oblong  2  inches  by  3 

inches  is  inches.     The  area  of  an  oblong  2 

inches  by  3  inches  is  sq.  in. 

7.  The  sum  of  two  numbers  is  16;  one  of  the 
numbers  is  9 ;  the  other  number  is -. 

8.  The  difference  of  two  numbers  is  5 ;  the  less 
number  is  11;  the  greater  number  is  . 


Copy  and  multiply: 

2Sj\  24.3 


33.3 

2 


24.4 

2 


12.2 
3 


74 


ELEMENTARY    ARITHMETIC. 


1.     4  inches)  12  inches 


This  means,  find  lioio  many  thnes  Jf  inches  are 
contained  in  12  inches.  Four  inches  are  contained 
in  12  inches  times. 


2.     4)12  inches 

This  means,  find  one  fourth  of  12  inches. 
fourth  of  12  inches  is  inches. 


One 


3.     4  inches)  16  inches 


This  means, 


This  means. 


4)16  inches 


5.  Hattie  lives  7  miles  south  of  Waukegan; 
Elsie  lives  9  miles  south  of  Hattie's  home;  from 
Waukegan  to  Elsie's  home  it  is miles. 

6.  When  the  top  of  the  mercury  column  in  a 
thermometer  is  at  32  degrees  above  zero,  water 
will  begin  to  freeze.  Thirty-two  degrees  above 
zero  is  called  "the  freezing  point."  When  the 
top  of  the  mercury  column  is  at  40  degrees  above 

zero,  it  is  degrees  above  the  freezing  point. 

When   the  top  of  the   mercury  column  is  at   26 

degrees  above  zero,  it  is  degrees  below  the 

freezing  point. 


Copy  and  divide: 
2  miles) 3 6  miles 


2  miles) 56  miles 


PART  II. 


75 


1 .  One  whole  is  twelfths. 

2.  One  half  is  twelfths. 

3.  One  fourth  is  :  twelfths. 

4.  Three  fourths  are  twelfths. 

5.  One  half  and  1  twelfth  are  twelfths. 

6.  One  half  and  5  twelfths  are  twelfths. 

7.  One  fourth  and  1  twelfth  are twelfths. 


twelfths, 
twelfth. 
—  twelfths. 


are 


8.  One  half  less  1  twelfth  are  

9.  One  half  less  5  twelfths  is  

10.  One  fourth  less  1  tweKth  are  — 

11.  Three    fourths    less    1    twelfth 
twelfths. 

12.  Two  times  5  twelfths  are  twelfths. 

13.  Three  times  2  twelfths  are  . 

14.  Two  twelfths  are  contained  in  1  half  — 
times. 


15.  One  third  of  1  fourth  is  — 

16.  Two  thirds  of  1  fourth  are 


Copy  and  divide: 


2)$46V 


TT 


2)$48.6  2)$62.4  2)$84. 


76 


ELEMENTARY    ARITHMETIC. 


njuzii 


\ » \ ,  \ 


are 


1.  One  inch  is  1  twelfth  of  a  foot. 

2.  One  half  of  a  foot  is twelfths  of  a  foot. 

3.  One  half  of  a  foot  and  1  twelfth  of  a  foot 
—  twelfths  of  a  foot. 


are 


4.  One  half  of  a  foot  and  5  twelfths  of  a  foot 
twelfths  of  a  foot. 

5.  One  half  of  a  foot  less  1  twelfth  of  a  foot 
—  twelfths  of  a  foot. 


are  — 

6.  One  half  of  a  foot  less  5  twelfths  of  a  foot 
is  twelfth  of  a  foot. 

7.  Two  times  5  twelfths  of  a  foot  are  

twelfths  of  a  foot. 

8.  Three  times  5  twelfths  of  a  foot  are  

twelfths  feet,  or  1  and  twelfths  feet. 

9.  Two  twelfths  of  a  foot  are  contained  in  1 
half  of  a  foot  times. 


Copy  and  add : 

32^            24.6 

33.8 

51.6 

42.7 

243-V            12.6 

24.5 

•     23.7 

23.7 

PART   II. 


77 


1.  Can  you  add  each  of  these 
cohimns  in  fifteen  seconds,  beginning 
at  the  top? 

2.  Can  you  add  each  of  these 
cohimns  in  fifteen  seconds,  beginning 
at  the  bottom? 

3.  Ten  threes  are  . 

4.  Fifteen  threes  are  . 

5.  Twenty  threes  are  . 


abed 


6.  Twenty-five  threes  are 

7.  Thirty  threes  are  

8.  Forty  threes  are  


9.  28  and  3  = 

10.  48  and  3  = 

11.  78  and  3  = 

12.  29  and  3  = 

13.  49  and  3  = 

14.  79  and  3  = 

15.  37  and  3  = 

16.  47  and  3  = 

17.  77  and  3  = 

18.  Three  lO's  : 

19.  Three  30's  : 


58  and  3  = 

38  and  3  = 

98  and  3  = 

59  and  3  = 

39  and  3  = 

99  and  3  = 

57  and  3  = 
67  and  3  = 
97  and  3  = 

3  20's  = 
3  40's  = 


3 
3 
3 
3 
3 
3 
3 
3 

o 
O 

o 
O 

o 
O 

3 
3 
3 
3 

o 
O 

3 


3  3 

o  o 

O  O 

3  3 

3  3 

3  3 

3  3 

3  3 

3  3 


3 
3 

2 
3 
1 
3 
2 
3 
1 
3 
2 
3 
2 
1 

o 
O 

3 
1 

2 

1  3 
3  3 
3  2 
3  2 
3  1 
3  3 
3  3 
3     2 


3 
3 
3 
3 
3 
3 
2 
3 
3 
3 
3 
3 
3 
3 
3 
3 

o 
O 


Copy  and  subtract: 

64  48  54 

21-1^  32.6  21.7 


57 
22.3 


45 
24.4 


78  ELEMENTARY    ARITHMETIC. 

1.  Four  quarts  and  1  pint  are  pints. 

2.  Four  gallons  and  1  quart  are  quarts. 

3.  Four  feet  and  1  inch  are  inches. 

4.  Four  yards  and  1  foot  are  —  feet. 

5.  Four  bushels  and  1  peck  are  pecks. 

6.  Four  nickels  and  1  cent  are  cents. 

7.  There  were  90  trees  in  an  orchard;  one 
third  of  them  were  apple  trees ;  one  third  of  them 
were  pear  trees,  and  the   remainder  were  peach 

trees.     There  were apple   trees,  pear 

trees,  and  peach  trees. 

8.  Three  fourths  of  the  trees  in  a  park  were 
maples;  the  remainder  were  oaks;  there  were  75 

maples.      There   were    trees    in   the    park. 

There  were  oaks  in  the  park. 

9.  Seventy-five  is  three  fourths  of  . 

10.  Thirty  is  three  fourths  of  . 

11.  William  bought  30  oranges  at  3  cents  each; 
he  gave  the  salesman  1  dollar;  he  should  receive 
in  change  cents. 

12.  Herbert  bought  2  packages  of  paper  at  20 
cents  each ;  he  gave  the  salesman  half  a  dollar ;  he 
should  receive  in  change  cents. 

13.  Twenty  3-cent  stamps  cost  cents. 

14.  For  90  cents  I  can  buy  3-cent  stamps. 

Copy  and  multiply  : 

223-V  32.7  24.5  31.6  43.7 

2  2  2  2  2 


PART  II.  79 

1.  Think  of  a  1-foot  square.    Think  of  a  3-foot 
square.      Think  of  a   3-foot   square  divided  into 

1-foot   squares.      A    3-foot    square    contains  

square  feet. 

2.  A  3-foot  square  is  sometimes  called  a  square 
yard.     A  square  yard  contains  square  feet. 

3.  One  third  of  a  square  yard  is  sq.  ft. 

4.  Two  thirds  of  a  square  yard  are  sq.  ft. 

5.  If  I  should  draw  an  oblong  3  feet  wide  and 
4  feet  long  and  divide  it  into  1-foot  squares  there 

would  be  rows  of  squares,  and  in  each  row 

there  would  be  squares.     An  oblong  3  feet 

by  4  feet  contains  square  feet. 

6.  Three  times  4  square  feet  are  sq.  it. 

7.  An  oblong  3  feet  by  4  feet  contains  1  and 
■ square  yards. 

8.  A  4-foot  square  contains  square  feet. 

9.  A  4-foot  square  contains  1  square  yard  and 
square  feet. 


10.  Six  square  feet  are of  a  square 

yard. 

11.  One   square  foot  is  contained  in  1   square 
yard  times. 

12.  Three  square  feet  are  contained  in  1  square 
yard  times. 

Copy  and  divide: 
2  tenths)36  tenths        .2)2.4^        .2)4.8        .2)6.4 

*  2  tenths  in  24  tenths. 


80 


ELEMENTARY    ARITHMETIC. 


1.  Write  the  following  in  figures,  using  tlie 
decimal  point: 

34  tenths  2  and  seven  tenths 

45  tenths  4  and  two  tenths 

23  tenths  3  and  five  tenths 

19  tenths  1  and  seven  tenths 

2.  Each  of  the  following  may  be  read  in  two 
ways: 

3.2  is  3  and  two  tenths,  or  32  tenths. 

2.7  is . 

5.1  is . 

4.4  is . 

3.  .3  are  contained  in  1.5  times. 

4.  .2  are  contained  in  1.6  times. 

5.  .4  are  contained  in  1.6  times. 

6.  .5  are  contained  in  1.5  times. 

7.  Draw  an  oblong  3  and  one  fourth  inches 
wide;  make  it  twice  as  long  as  it  is  wide;  it  is 
' and  inches  long. 

8.  Draw  an  oblong  4  and  one  half  inches  wide; 

make  it  twice  as  long  as  it  is  wide;    it  is  

inches  long. 

9.  I  of  12  are  .         12  is  f  of  . 

10.  i  of  12  is  .  12  is  i  of  . 


Copy  and  divide : 

2)$46|-  2)$48.4 


2)$28|-  2)$68.2 


PART  II. 

9 

•^             3  sixes  are  18 

8 

6  threes  axe  18 

T 

i  Q             9  twos  are  18 

81 


17 

1.  Nine  and  8  are  

2.  Nine  and  7  are  

3.  Seventeen  less  8  are 

4.  Seventeen  less  7  are 

5.  Eio^liteen  less  9  are  - 

6.  Eig:liteen  less  8  are  - 


7.  18  is 


9's. 


8.  Seventeen  inches  are 

9.  Seventeen  dimes  are 

10.  Seventeen  days  are  - 

11.  Seventeen  pints  are  - 

12.  Seventeen  quarts  are 

13.  Seventeen  quarts  are 

14.  Seventeen  feet  are  — 

15.  Eighteen  tenths  are  - 

16.  Ei2;hteen  fifths  are  — 

17.  Eis^hteen  fourths  are 

18.  Eighteen  feet  are  — 

19.  Eiofhteen  cents  are  — 

20.  Eighteen  days  are  — 


9  and  9  are  

9  and  6  are  

-.     17  less  12  = 
-.     17  less  11  = 
18  less  12  .= 
18  less  15  = 


18  is 


6's. 


-  foot  and  - 

-  dollar  and 
weeks  and  - 

-  quarts  and 

-  pecks  and 

-  gallons  and 
yards  and  — 

-  and  . 

and  -. 

-  and  -. 


yards, 
dime  and 
weeks  and 


Copy  and  add: 

35i              43.2 

37.3 

46.4 

55.6 

36i              29.1 

27.4 

28.2 

17.1 

S2 


ELEMEKTAEY   AKITHMETIC. 


9 

9 

8 

7 

4 

6 

8 

6 

9 

7 

9 

8 

9 

7 

7 

6 

8 

8 

9 

9 

5 

7 

5 

8 

FOR    DRILL    IN    ADDING. 


Review  and  drill  until  pupils  can  give 
the  sums  in  any  order  in  12  seconds.  It 
provides  an  excellent  exercise  to  put  the 
figures  found  in  this  table  upon  12  cards, 
2  figures  on  each  card;  then  allow  the 
pupils  to  handle  the  cards  and  name  the 
sums  as  rapidly  as  possible. 

Suspend  a  pendulum  39  inches  long, 
and  see  how  many  pupils  can  recite 
these  sums  while  it  vibrates  12  times. 


FOR    DRILL    IN    MULTIPLYING. 


This  is  a  review  of  the  23  facts  of  multiplication  that   have 
already  been  presented. 


2  times  2  are 

4  times  2  are 

6  times  2  are 

3  times  2  are 

5  times  2  are 

8  times  2  are 

7  times  2  are 

9  times  2  are 

3  times  3  are 
2  times  4  are 
2  times  3  are 

4  times  4  are 


2  times  5  are 

3  times  6  are 

2  times  7  are 

3  times  5  are 
2  times  9  are 
2  times  8  are 

2  times  6  are 

4  times  3  are 

5  times  3  are 

6  times  3  are 

3  times  4  are 


Copy  and  subtract: 

43      35 

21|      12| 


57 
23| 


48 
31f 


59 

24.6 


PART  II.  83 

1.  Henry  drew  an  oblong  upon  his  slate.  It 
contained  10  square  inches.  It  was  5  inches  long. 
It  was  inches  wide. 

2.  A  square  that  contains  4  square  inches  is  a 

inch  square. 

3.  A  square  that  contains  9  square  inches  is  a 

inch  square. 


4.  Mary  drew  a  square  upon  her  slate;  the 
area  of  the  square  was  16  square  inches.  It  was 
a<  square  inch. 

5.  The  sum  of  8  cents  and  2  cents  is  ^. 

6.  The  difference  of  8  cents  and  2  cents  is 
cents. 

7.  There  can  he  7io  j^roduct  of  8  cents  and  2  cents. 

8.  The  product  of  8  cents  and  2  is  ^. 

9.  The  quotient  of  8^  divided  by  2^  is  . 

10.  The  quotient  of  8^  divided  by  2  is  


11.  The  quotient  of  15^  divided  by  3^  is  

12.  The  quotient  of  15^  divided  by  3  is  ^ 

13.  The  quotient  of  16^  divided  by  4^  is 


14.  The  quotient  of  16^  divided  by  4  is  ^ 

15.  The  quotient  of  15^  divided  by  5^  is  — 

16.  The  quotient  of  15^  divided  by  5  is  


Copy  and  multiply : 
\^  321 

3  2  2  2  3 


22|  32|-  43|-  21|-  21.6 


84  ELEMENTARY    ARITHMETIC. 

1.  5  quarts)  15  quarts 

This  means,  find  how  r}iany  thnes  5  quarts  are 
contained  in  1 5  quarts.  Five  quarts  are  contained 
in  15  quarts  times. 

2.  5)15  quarts 

This  means,  find  one  fifth  of  15  quarts.  One 
fifth  of  15  quarts  is  quarts. 

3.  Highland  Park  is  11  miles  north  of  Evans- 
ton;  Waukegan  is  12^  miles  north  of  Highland 

Park ;    from  Evanston  to  Waukegan  it  is   

miles. 

4.  In  the  evening  the  outdoor  temperature  was 
8  degrees  above  the  freezing  point ;  the  next  morn- 
ing it  was  9  degrees  below  the  freezing  point; 
during  the  night  it  had  fallen  degrees. 

5.  When  the  temperature  is  2  degrees  below 
the  freezing  point,  it  is  degrees  above  zero. 

6.  When  the  temperature  is  28  degrees  above 
zero,  it  is  degrees  below  the  freezing  point. 

7.  18  is  4  4's  and .     18  is  3  5's  and . 

8.  18  is  2  7's  and .     18  is  2  8's  and . 

9.  17  is  8  2's  and .     17  is  5  3's  and . 


10.  17  is  7  2's  and .     17  is  2  6's  and . 

Copy  and  divide : 

3  fifths)15  fifths  3  fourths)18  fourths 

3  halves) 3 6  halves  3  tenths) 3 6  tenths 


PART  II. 


85 


thirds. 

sixths, 
sixths. 
—  sixths. 


1.  One  whole  is  — 

2.  One  whole  is  — 

3.  One  third  is  — 

4.  Two  thirds  are 

5.  One  third  and  1  sixth  are  - 

6.  Two  thirds  and  1  sixth  are 

7.  One  third  less  1  sixth  is  — 

8.  Two  thirds  less  1  sixth  are 

9.  Two  times  2  sixths  are  — 
10.  Three  times  2  sixths  are  — 


sixths. 
-  sixths. 


sixth. 
—  sixths. 


sixths. 


11.  Two    sixths    are     contained    in    1    whole 


12.  One  half  of  1  third  is  

sixth. 

13.  1  and  |  = 

4-  less  1  = 

1  and  1  == 

14.  4-  less   1  = 

4"  and  i  = 

|less   1  = 

15.  1  and  ^V  = 

1  ipcjtj    1    ._ 
-g-  less  YlT  — 

4"  and  y^^  = 

16.  1  less  yV  = 

4-  and  1  = 

-g-  less   -^  = 

17.  i  and  -^\  = 

Y  ^^^^  T^  = 

i  and  ,%  - 

18.   I  less  ,V  - 

1  and  3^  - 

■F  1^^^  TO"  = 

Copy  and  divide: 

2)24  thirds 

2)46  tenths 

3)36  fifths 

86  ELEMENTARY    ARITHMETIC. 


1.  One  third  of  a  pie  is  2  sixths  of  a  pie. 

2.  Two  thirds  of  a  pie  are  4  sixths  of  a  pie. 

3 .  Harry  had  a  whole  pie ;  he  ate  1  third  of  it 
for  his  lunch  and  1  sixth  of  it  at  dinner  time ;  he 
then  had of  a  pie. 

4.  Sarah  had  1  third  of  a  -pie;  she  gave  1  sixth 

of  a  pie  to  her  little  brother ;  she  then  had  

of  a  pie. 

5.  Mrs.  Smith's  boarders  ate  2^  pies  at  dinner 

and  2^  pies  at  supper;  in  all  they  ate  

pies. 

6.  Hattie  divided  2^  pies  among  her  play- 
mates, giving  to  each  ^  of  a  pie;    she  had  

playmates. 

7.  If  I  should  divide  1  half  of  a  pie  equally 
among  three  children,  each  child  would  receive 
of  a  pie. 

8.  If  I  should  divide  1  half  of  a  pie  equally 
between  two  children,  each  child  would  receive 
of  a  pie. 

9.  If  I  had  two  thirds  of  a  pie  and  gave  away 

1  sixth  of  a  pie,  I  should  then  have of 

a  pie. 

Copy  and  add: 

24|      261      245      374      18.6 
32|      162      182      131      32.2 


PART    II. 

87 

1.  Can  you  add  each  of   these 

cohimns   in   fifteen 
mng  at  the  top? 

seconds,  begin- 

a 
4 

b 

2 

c 
4 

d 
3 

2.  Can  vou  add 
cohimns    m   fifteen 

[   each  of   these 
seconds,  begm- 

4 
4 
4 

4 
4 
4 

4 
4 
4 

4 

2 

1 

ning  at  the  bottom? 

4 

4 

1 

1 

4 

4 

4 

3 

3.  Ten  fours  are 

. 

4 

4 

4 

4 

4.  Eleven  fours  ; 

are  -. 

4 

4 

4 

2 

5.  Twelve  fours 

are  . 

4 
4 

4 
4 

4 

2 

3 
1 

6.  28  and  4  = 

38  and  4  =. 

4 

4 

4 

4 

7.  48  a.nd  4  = 

58  and  4  = 

4 
4 
4 

4 
4 
4 

4 
4 
4 

2 
2 
1 

8.  68  and  4  = 

78  and  4  = 

9.  29  and  4  = 

39  and  4  = 

4 
4 

4 
4 

4 
4 

3 

4 

10.  49  and  4  = 

59  and  4  = 

JL 

4 

4 

_L 

4 

2 

11.  69  and  4  = 

79  and  4  = 

4 

4 

3 

4 

4 

4 

4 

3 

12.  26  and  4  = 

36  and  4  = 

4 

4 

4 

1 

13.  46  and  4  = 

56  and  4  = 

4 

4 

4 

2 

14.  66  and  4  = 

76  and  4  =: 

4 

4 

4 
4 

4 
4 

4 

2 

15.  27  and  4  = 

37  and  4  = 

4 

4 

4 

3 

16.  47  and  4  = 

57  and  4  = 

1 

3 

4 

4 

17.  67  and  4  = 

77  and  4  = 

Copy  and  subtract: 

247              209 

207              325 

346 

63                82 

43                62 

84 

88  ELEMENTARY    ARITHMETIC. 

1.  Five  quarts  and  1  pint  are pints. 

2.  Five  yards  and  1  foot  are  feet. 

3.  Five  dimes  and  1  cent  are  cents. 

4.  Five  halves  and  1  fourth  are  fourths. 

5.  Five  halves  and  1  sixth  are  sixths. 

6.  Five  nickels  and  1  cent  are  cents. 

7.  Seven  pints  are and quarts. 

8.  Two  is  contained  in  7 times. 

9.  Two  is  contained  in  9  times. 

10.  Seven  feet  are  and yards. 

11.  Three  is  contained  in  7  times. 

12.  Three  is  contained  in  10  times. 

13.  Nine  pecks  are and bushels. 

14.  Four  is  contained  in  9   times. 

15.  Four  is  contained  in  13  times. 

16.  In  11  there  are  — 5's  and  remain- 
der. 

17.  Five  is  contained  in  11  times. 

18.  Five  is  contained  in  16   times. 

19.  In  13  there  are  6's  and  remain- 
der. 

20.  Six  is  contained  in  13  times. 

21.  Six  is  contained  in  19  times. 


283  25.3 

2  2 


Copy  and  multiply : 

32i              263 
3                    2 

273 

2 

PART  II.  89 

1.  8  +  2,  means,  8  and  2 ;  8  and  2  are  . 

2.  8  —  2,  means,  8  less  2;  8  less  2  are  . 

3.  8  inches  x  2,  means,  2  times  8  inches;  2 
times  8  inches  are  — - — -  inches. 

4.  8  inches  -^  2  inches,  means,  find  lioio  many 
times  2  inches  are  contained  in  8  inches;  2  inches 
are  contained  in  8  inches  times. 

5.  8  inches  ^  2,  means,  ^nc?  one  half  of  8  inches; 
one  half  of  8  inches  is  inches. 

6.  4  sixths  +  2  sixths,  means  

7.  4  sixths  —  2  sixths,  means  

8.  4  sixths  X  2,  means  . 

9.  4  sixths  -=-  2  sixths,  means  


10.  4  sixths  -^  2,  means  . 

11.  6  tenths  +  2  tenths,  means 

12.  6  tenths  —  2  tenths,  means 

13.  6  tenths  x  2,  means  . 

14.  6  tenths  ~  2  tenths,  means 

15.  6  tenths  -^  2,  means  . 


16.  12^  +  3^,  means  .       12^ 


^+ 

2    _ 

T  — 

4 

2    — 
6 

|x 

2  = 

4      . 

2    — 

4     . 
"B"  ~ 

2  = 

.6  + 

.2  = 

,6- 

.2  = 

.6  X 

2  = 

.6- 

.2  = 

.6- 

2  = 

D(t,  means 

17.  12^  X  3^  =  nonsense.     12^  x  3,  means 

18.  12^  -^  3,    means  .       12^  -^  3^,    means 


Copy  and  divide: 

$4)$804         $4)$408         $4)$448         $4)$488 
- —  times 


90  ELEMENTARY    ARITHMETIC. 

1.  Write   the  following  in   figures,  using  the 
decimal  point: 

275  tenths  23  and  4  tenths 

146  tenths  13  and  5  tenths 

224  tenths  26  and  3  tenths 

346  tenths  15  and  6  tenths 

2.  Each  of  the  following  may  be  read  in  two 
ways : 

24.2  is  24  and  2  tenths,  or  242  tenths. 

37.5  is  — — . 

25.6  is . 

14.5  is . 

3.  Draw  an  oblong  6  and  1  half  inches  long; 

make  it  one  half  as  wide  as  it  is  long;  it  is  

and  inches  wide. 

6  J  inches  h-  2  means  .     6^  inches  ^  2  = 

4.  Draw  an  oblong  4  and  1  half  inches  long; 

make  it  half  as  wide  as  it  is  long;    it  is  

and inches  wide. 

4J  inches  -^  2  means  -.     4^  inches  -i-  2  = 

5.  f  of  12  are  .         12  is  f  of  . 

6.  J  of    8  are  .  9  is  f  of  . 

7.  i  of    7  is  .  7  is  i  of  . 

Copy  and  divide : 

4)$804     4)$408     4)$448^     4)$488 


PART  II. 


91 


4  fives  are  20 
3  sevens  are  21 
3  eights  are  24 

1.  Twenty  pecks  are  

2.  Twenty  fifths  are  

3.  Twenty-one  days  are  — 

4.  Twenty-one  feet  are  — 

5.  Twenty-four  quarts  are 

6.  Twenty-fonr  feet  are  — 


5  fours  are  20 

7  threes  are  21 

8  threes  are  24 


bushels, 
wholes. 

—  weeks. 

—  yards. 

pecks. 


yards. 


7.  Three  pecks  are  

8.  Three  weeks  are  — 

9.  Eight  yards  are  

10.  Five  bushels  are  — 

11.  Nineteen  inches  are 

12.  Nineteen  quarts  are 

13.  Twenty  days  are  — 
14. 
15. 


quarts. 

days, 
feet. 

pecks. 


2  pecks  = 
2  weeks  = 
7  yards  = 
4  bushels  = 


Twenty-one  dimes  are  — 
Twenty-two  pecks  are  — 

16.  Twenty-two  feet  are  — 

17.  Twenty-four  cents  are  - 

18.  Twenty-four  tenths  are 


—  foot  and  — 

—  pecks  and  - 

weeks  and  

dollars  and 

bushels  and 

—  yards  and 
dimes  and 

—  and  


and 


19.  Twenty-four  sevenths  are  - 

20.  Twenty-four  fifths  are  

21.  Twenty-four  days  are weeks  and 


and 


Copy  and  add: 

23i      362 

375 

284 

27.4 

35i      241 

143 

172 

35.1 

92  ELEMENTARY    ARITHMETIC. 

1.  Twelve  pairs  of  boots  are  boots. 

2.  Three  spiders  have  legs. 

3.  Three  house-flies  have  legs. 

4.  Three  cats  have  feet. 

5.  Eleven  spans  of  horses  are  horses. 

6.  Five  butterflies  have  wings. 

7.  A  cat  has  toes  on  each  front  foot  and 

toes  on  each  hind  foot.    A  cat  has toes. 


8.  Eight  three-cent  stamps  cost  cents. 

9.  Eight  2-cent  stamps  cost  cents. 

10.  A  boy  wears  2   shoes.     A  horse  wears  4 
shoes.     An  ox  wears  8  shoes.     Three  boys  need 

shoes.     3  horses  need  shoes.     3  oxen 

need  shoes. 

11.  What  day  of  the  week  is  it?     It  is . 


One  week  from  to-day  will  be  ;  14  days 

from  to-day  will  be  ;  21  days  from  to- 
day will  be  ;    22  days  from  to-day  will 

be ;  20  days  from  to-day  will  be . 

12.  At  3^  each,  7  oranges  cost  cents. 

13.  At  8^  each,  3  melons  cost  cents. 

14.  At  7^  each,  3  balls  cost  cents. 

15.  At  3^  each,  8  pencils  cost  cents. 

16.  When  2  oranges  cost  8^,  3  oranges  cost . 

^17.  When  3  lemons  cost  6^,  4  lemons  cost . 


Copy  and  subtract: 

45i      264      363      268      36.5 

17i      83      91      72      8.2 


PART  II.  93 

1.  Henry  drew  an  oblong  upon  liis  slate.  It 
contained  20  square  inches.  It  Avas  5  inches  long. 
It  was  inches  wide. 

2.  An  oblong  that  is  3  inches  by  7  inches  con- 
tains    square  inches.     Its  perimeter  is  

inches. 

3.  The  area  of  an  oblong  that  is  2  inches  by  8 
inches  is  square  inches.     8  sq.  in.  x  2  = 

4.  The  perimeter  of  an  oblong  that  is  2  inches 
by  8  inches  is  inches. 

5.  A  square  whose  area  is  16  square  inches  is 
a  inch  square. 

6.  I  am  thinking  of  an  oblong  whose  area  is 

21  square  inches.     It  is  7  inches  long.     It  is  

inches  wide. 

7.  The  perimeter  of  a  figure  is  18  feet;  each 
side  is  6  feet;  the  figure  is  a  . 

8.  The  sum  of  10  feet  and  2  feet  is  ft. 

9.  The  difference  of  10  feet  and  2  feet  is  

ft. 

10.  There  can  he  no  product  of  10  feet  and  ^  feet. 

11.  The  product  of  10  feet  and  2  is  ft. 

12.  The  quotient  of  10  feet  divided  by  2  feet  is 


13.  The    quotient  of  10  feet  divided  by  2  is 
—  ft. 


Copy  and  multiply: 

22^  132  231  123  12.3 

4  4  4  4  4 


94  ELEMENTARY    ARITHMETIC. 

1.  3  pecks) 24  pecks 

This  means,  find  how  many  times  8  jpecks  are 
contained  in  ^^  pecks.  Three  pecks  are  contained 
in  24  pecks  times. 

2.  3)24  pecks 

This  means,  find  one  third  of  ^Jf  pecks.  One 
third  of  24  pecks  is  pecks. 

3.  Peter  lives  4^  miles  west  of  Lake  Michigan; 
Herbert  lives  2f  miles  west  of  Peter  \  Herbert  lives 
miles  west  of  the  lake. 

4.  When  the  temperature  is  6  degrees  below 
the  freezing  |)oint,  it  is  • degrees  above  zero. 

5.  Samuel  has  two  pieces  of  rope;  one  piece 
is  8  feet  long;  the  other  piece  is  3  yards  long; 
together  they  are  feet  long. 

6.  AYlien  apples  cost  2^  dollars  a  barrel,  3 
barrels  cost  dollars. 

7.  I  am  thinking  of  a  triangle,  each  side  of 
which  is  2  inches  long.  The  perimeter  of  the 
triangle  is  inches. 

8.  I  am  thinking  of  a  triangle,  each  side  of 
which  is  4  feet  long.  The  perimeter  of  the  triangle 
is  feet. 

9.  Twelve  feet  equal  yards. 

Copy  and  divide: 

$3)$426         $3)$456         $3)$486         $3)$786 
times 


PART  II. 


95 


1.  One  whole  is 

2.  One  third  is 


ninths, 
ninths. 
— ■  ninths. 


3.  Two  thirds  are  — 

4.  One  third  and  1  ninth  are  — 

5.  One  third  less  1  ninth  are  — 

6.  Two  thirds  and  1  ninth  are 

7.  Two  thirds  less  1  ninth  are  - 

8.  One  third  and  2  ninths  are  - 

9.  One  third  less  2  ninths  is  — 

10.  Two  thirds  and  2  ninths  are 

11.  Two  thirds  less  2  ninths  are 


12.  Four  times  2  ninths  are  - 

13.  Three  times  2  ninths  are 


ninths, 
ninths. 

—  ninths. 

—  ninths. 

—  ninths, 
ninth. 

—  ninths. 

—  ninths. 


ninths. 
-  ninths. 


14.  Two  ninths  are  contained  in  8  ninths  

times. 

15.  Two  ninths  are  contained  in  1^^  times. 


16.  One  half  of  1  third  is 

17.  One  third  of  1  third  is 


Copy  and  divide: 

3)$426     3)$456 


3)$486 


3)$786 


96  ELEMENTARY    ARITHMETIC. 

1.  If  each  third  of  a  pie  should  be  divided  into 

3  equal  pieces,  each  piece  would  be of 

a  pie.      A  hungry  boy  would   think   these  very 
small  pieces. 

2 .  4^  of  a  pie  -\-^  oi  Si  pie  =  2|  +  2^  — 

3.  ^  oi  Sb  pie  —  -^  of  a  pie  =  4|  —  2^  = 

4.  2f  of  a  pie  X  4  =  3f  x  4    = 

5.  2^  pies  -^  ^  oi  a,  pie  =  2|  -^  4-    = 

6.  4|  pies  -  2  =  8|  -  2    = 


7.  I  of  a  yard  and  -J-  of  a  yard  =  2|  +  2|-  = 

8.  |-  of  a  yard  less  -g-  of  a  yard  =  4f  —  2^  = 

9.  I  of  a  yard  x  3  =  2|-  x  3    = 

10.  1-^  yards  -^  i  of  a  yard  =  2^  -^  4-    = 

11.  6|  yards -3:=  9|  -  3    = 

12.  Henry  had  two  pieces  of  rope;  one  was  2^ 
yards  long ;  the  other  was  3|-  yards  long ;  together 
they  were  and yards  long. 

13.  One  and  -^  yards  and  1^  yards  are  . 

14.  The  sum  of  5|  yards  and  2^  yards  is  

and  yards. 

15.  One  foot  is of  a  yard. 

16.  One  third  of  a  foot  is  1  ninth  of  a  yard. 


Copy  and  add: 

34|      624 

736 

832 

92.2 

23|      625 

721 

822 

93.5 

PART  II.  97 

1.  Can  you  add  column  (a)  in  fifteen  seconds, 
beginning  at  the  top? 

2.  Can  you  add  column  (a)  in  fifteen  seconds, 
beginning  at  the  bottom? 

3 .  Practice  until  you  can  do 
this  with  each  column. 

4.  Ten  fives  are  . 


5.  Eleven  fives  are  

6.  Twelve  fives  are  — 

7.  Twenty  fives  are  — 

8.  28  +  5=        38  +  5 

9.  48  +  5=        58  +  5 

10.  68  +  5=        78  +  5 

11.  19  +  5=        39  +  5 

12.  49  +  5=        29  +  5 

13.  69  +  5=        89  +  5 

14.  67  +  5=        37  +  5 

15.  27  +  5=        17  +  5 


16.  16  +  5  = 

36  +  5: 

17.  26  +  5  = 

56   +  5: 

Copy  and  subtract : 

54|             253 

355 

26|                72 

82 

a 

b 

c 

d 

e 

5 

2 

4 

5 

5 

5 

5 

5 

5 

4 

5 

5 

5 

5 

3 

5 

5 

5 

4 

2 

5 

5 

5 

5 

1 

5 

6 

5 

5 

3 

5 

5 

5 

5 

4 

5 

0 

5 

3 

2 

5 

5 

5 

5 

5 

5 

5 

5 

5 

1 

5 

5 

5 

5 

5 

5 

5 

5 

2 

3 

5 

5 

5 

5 

4 

5 

5 

5 

5 

2 

5 

5 

5 

5 

1 

5 

5 

5 

1 

5 

5 

5 

5 

5 

4 

5 

5 

5 

5 

2 

5 

5 

5 

5 

3 

5 

5 

5 

4 

4 

1 

3 

0 

5 

3 

257 

24.6 

92 

8.2 

98 


ELEMENTARY    ARITHMETIC. 


1.  Six  quarts  and  1  pint  are  pints. 

2.  Six  yards  and  1  foot  are  ■  feet. 

3.  Six  dimes  and  1  cent  are  cents. 

4.  Six  halves  and  1  fourth  are  fourths. 

5.  Six  nickels  and  1  cent  are  ■ cents. 


6.  Eight  feet  are  and 

7.  Three  is  contained  in  8  - 

8.  Three  is  contained  in  11 

9.  Ten  pecks  are and  - 

10.  Four  is  contained  in  10  - 

11.  Four  is  contained  in  14  - 


12. 

der. 


In  12  there  are 


5's  and 


13.  Five  is  contained  in  12 

14.  Five  is  contained  in  17 

15.  Five  is  contained  in  21 

16.  Five  is  contained  in  22 

17.  Five  is  contained  in  23 

18.  Five  is  contained  in  24 


—  yards, 
times. 

times. 

-  bushels. 


times, 
times. 

-  remain- 


times, 
times, 
times, 
times, 
times, 
times. 


19.  4  12's  are  48. 

20.  4  ll's  are  44. 

21.  3  ll's  are  33. 

Copy  and  multiply : 

231  104 

5  5 


5  12'sare  60 
5  ll's  are  55. 
2  ll's  are  22. 


103 
5 


102 

5 


10.5 
5 


PART    II. 


99 


1.  $9  +  $7,  means 

2. 

3. 

4.  $9 


—  ^i ,  means 
X  2,  means  - 


$2,  means 


5. 

6. 
7. 
8. 
9. 
10. 

11. 
12. 
13. 


^  9, 


means 


1  05 


means 


11+ 

)|-  —  $y\j-j  means 
)^  X  5,  means  - 


9 
TIT 


)y%,  means 


'T 


^Q-  -=-  2,  means 


$9  and  $7  = 
$9  less  $7  =. 
2  times  $9  = 

$2  are  . 

I-  of  $9  = 

$i  and  -$yV  = 
$i  less  $yV  = 
5  times  $yV  = 
$yV  are . 

iof  $A  = 


..6  +  $.3,  means  - 
•  1  —  $.3,  means  - 
1.5  X  4,  means  — 

14.  $1.5  -  $.3,  means 

15.  $1.8  -^  3,  means  — 


.3 


$.6  + 
$1-! 
4  times  $.5  = 


.3 


.3  are 


16.  Arthur  had 
had  and  — 


.2;  he  earned 
dollars. 


I  of 


1.5:  he  then 


17.  Fred  had  $3.6;  he  spent  $1.5;  he  then  had 
—  and dollars. 


18.  James  earned  $.3  each  day;  in  4  days  he 
earned  . 

19.  When  coffee  costs  $.3  a  pomid,  for  $1.2  I 
can  buy  pounds. 

Copy  and  divide : 

$2)$412         $2)$616         $2)$214        $2)$418 
times 


100 


ELEMENTARY    ARITHMETIC. 


1. 

2. 
3. 
4. 
5. 
6. 


60  seconds  are  1  minute. 
60  minutes  are  1  hour. 
24  hours  are  1  day. 


One  half-hour  is  — 
One  fourth-hour  is 


minutes. 
—  minutes. 


When  the  long  hand  of  a  clock  points  to 
KII  and  the  short  hand  to  IX,  it  is  o'clock. 

7.  When  the  long  hand  points  to  XII  and  the 
short  hand  to  Yl,  it  is  o'clock. 

8.  At  5  minutes  past  9,  the  long  hand  points  to 

.      At  "  half  past    3/'  the  long  hand  points 

to  .      At  "  quarter  past   6/'   the  long  hand 

points  to  .     At  20  minutes  past  8,  the  long 

hand  points  to  . 

9.  ''  Half  past  9  "  is  usually  printed  9:30. 

10.  "  Quarter  past  9  "  is  usually  printed  9:15. 

11.  ''  Quarter  of  ten  "  is  usually  printed  9:45. 


Copy  and  divide: 

2)$412     2)$616 


2^S214 


2)$418 


PART  II. 

4  sixes  are  24      6  fours  are  24 

3  nines  are  27      9  threes  are  27 

5  fives  are  25 


^    '  101 


1.  Twenty-four  pecks  are  — 

2.  Twenty-four  sixths  are  - 

3.  Twenty-seven  feet  are  — 

4.  Twenty-seven  ninths  are 

5.  Twenty-five  fifths  are  — 


bushels. 

-  wholes, 
yards. 

—  wholes, 
wholes. 


6.  25  is 

7.  27  is 

8.  28  is 

9.  29  is 


6's  and 
4's  and 
9's  and 
6's  and 


26  is 
26  is 

29  is 
29  is 


4's  and 
6's  and 
3's  and 
4's  and 


10.  6  bushels  are 

11.  9  yards  are  - 


pecks. 


feet. 


12.  Twenty-five  inches  are 

13.  Twenty-five  quarts  are 

14.  Twenty-six  days  are  — 


5  bushels 
8  yards  = 

—  feet  and 

—  pecks  and 
weeks  and  - 

—  dollars  and 


15.  Twenty-six  dimes  are  — 

16.  Six  bushels  and  2  pecks  are  pecks. 

17.  Five  bushels  and  3  pecks  are  pecks. 

18.  Nine  yards  and  2  feet  are  feet. 

19.  Eight  yards  and  1  foot  are  feet. 

20.  Three  feet  and  3  inches  are  inches. 


26| 
221 


Copy  and  add: 

605 

508 


704 

609 


803 
708 


90.7 
60.5 


102  ELEMENTARY    ARITHMETIC. 

1.  Two  tliirds  of  18  apples  are  apples. 

2.  Eighteen  apples  are  two  tliirds  of  . 

3.  Three  fourths  of  12  oranges  are  or- 
anges. 

4.  Twelve  oranges  are  three  fourths  of ■. 

5.  Eight  is  two  thirds   of    .     12   is  two 

thirds  of  .     18  is  two  thirds  of  . 

6.  The  first  day  of  August,  1898,  was  Monday; 
the  next  Monday  was  the  th ;  the  ninth  was 

;  the  seventh  was  . 

7.  Nine  3-cent  stamps  cost cents. 

8.  Six  4-cent  stamps  cost  cents. 

9.  Five  5-cent  stamps  cost  cents. 

10.  At  $9  a  ton,  3  tons  of  hay  cost dollars. 

11.  At  $6  a  ton,  4  tons  of  coal  cost dollars. 

12.  At  $3  each,  9  hats  cost dollars. 

13.  Six  spoons  are  a  set;  24  spoons  are  — 

sets;  18  spoons  are  sets. 

14.  When  kerosene  is  9^  a  gallon,  for  27^  I  can 
buy gallons. 

15.  When  wood  is  $6  a  cord,  for  $24  I  can  buy 
cords;  for  $27  I  can  buy  cords. 

16.  When  sugar  is  4^  a  pound,  for  24^  I  can 

buy  pounds;    for  26^  I  can  buy  

pounds. 


383  32.6 

191  16.3 


Copy  and  subtract: 

62|              365 

374 

16^              183 

182 

PART    II.  103 

1.  If  I  should  draw  an  oblong  3  inches  wide 
and  9  inches  long,  and  then  divide  it  into  1-inch 

squares,    there   would    be  ■ •  rows    of    squares. 

An  oblong  3   inches  by   9   inches   contains  

square  inches. 

2.  Three  times  9  square  inches  are  . 

3.  Nine  times  3  square  inches  are  . 

4.  A  square  whose  area  is  25  square  inches  is 
a  inch  square. 

5.  The  perimeter  of  a  5-inch  square  is  

inches. 

6.  I  am  thinking  of  a  pentagon,  each  side  of 
which  is  4  inches.  The  perimeter  of  this  pentagon 
is  inches. 

7.  The  sum  of  9  inches  and  3  inches  = 

8.  The  difference  of  9  inches  and  3  inches  = 

9.  There  can  he  no  'product  of  9  inches  and  3 
inches. 

10.  The  product  of  9  inches  and  3  = 

11.  The   quotient   of    27    inches    divided    by  3 
inches  = 

12.  The  quotient  of  27  inches  divided  by  3  = 

13.  The  quotient   of    24    inches    divided   by  4 
inches  = 

14.  The  quotient  of  24  inches  divided  by  4  = 


Copy  and  multiply : 

311              131 

141 

151 

12.1 

5                   5 

5 

0 

5 

104  ELEMEN^TARY    ARITHMETIC. 

1.  Four  and  one  half  times  6,  means,  Jf  sixes 
and  1  half  of  six.     4^  times  6  = 

2.  6  X  2^,  means,  2^  times  6,  or  2  sixes  and  \ 
of  six.     2  J  times  6  —  6x2^  — 

3.  Notice  carefully  the  following: 

3  tons  at  $8  a  ton;  $8x3  = 
2  tons  at  $8  a  ton;  $8x2  = 
1  ton  at  $8  a  ton;  $8x1  = 
i  ton  at  $8  a  ton;  $8  x  i  = 
i  ton  at  $8  a  ton;  $8  x  i  = 
21  tons  at  $8  a  ton;  $8  x  2i  = 
2i  tons  at  $8  a  ton;     $8  x  2i  = 

4.  Remeiiiber  that  to  niidtiioly  a  number  hy  \  is 
to  (jet  i  of  that  number;  to  multiply  by  J . 

5.  10  X  i,   means,    ^   of  ten.     10  x  |,    means 


6.  10  multiplied  by  2^  = 

7.  12  multiplied  by  2^  = 

8.  20  multiplied  by  2i  = 

9.  30  multiplied  by  2^  = 

10.  4  X  21=  5  X  21  = 

11.  3  X  24=  7  X  21  = 

12.  At    $6    a   ton,   2^   tons   of  coal  cost  

dollars. 

Copy  and  divide: 

$4)$524    $4)$564    $4)$604    $4)$608 

*  The  sign  of  multiplicatiou  in  this  book  is  to  be  read  multi- 
plied by. 


PART  II. 


105 


1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 
10. 
11. 
12. 
13. 
14. 
15. 
16. 
times. 
17. 
18. 
19. 
20. 


One  whole  is  - 
One  fifth  is  — 
Two  fifths  are 


-  tenths, 
tenths. 

-  tenths, 

tentlis. 


—  tenths. 


Three  fiftlis  are 

Four  fifths  are  - 

One  fifth  and  1  tenth  are 

One  fifth  less  1  tenth  is  - 


tenths. 


tenth. 

tenths, 

tenths. 

—  tenths. 

—  tenths. 
Four  fifths  and  three  tenths  are tenths. 


Three  fifths  and  1  tenth  are 
Three  fifths  less  1  tenth  are 
Four  fifths  and  1  tenth  are 
Four  fifths  less  1  tenth  are 


Four  fifths  less  3  tenths  are 
Four  times  2  tenths  are  - — - 
Three  times  3  tenths  are  — 


tenths. 


—  tenths. 

—  tenths. 
Two  tenths  are  contained  in  6  tenths 


One  tenth  is  contained  in  1  fifth 

One  half  of  1  fifth  is 

One  half  of  3  fifths  is  

One  half  of  2  fifths  is 


times. 


Copy  and  divide: 

4)$524     4)$564 


4)$604 


4)$608 


106  ELEMENTARY    ARITHMETIC. 

[   I  I   I  I   [TT  I  I   I  I  I   I  I   I  I   iq: 


1 .  Sometimes  inches  are  divided  into  fifths  and 
tenths.  Perhaps  the  teacher  can  show  you  a  rule 
so  divided. 

2.  -^  of  an  inch  +  y^  of  ^^  i^-  =       ^i  +  ^tw  — 

3.  4-  of  an  inch  —  -^^  of  an  in.  =       i\  —  2^^^  = 

4.  yV  c>f  an  inch  x  3  =  2^^^  x  3  = 

5.  2|-  in.  ^  4^  of  an  inch  =  1|  -^  y^  = 

6.  6|in. -2=  8|-2  = 

7.  Draw  a  line  3  inches  long;    erase  from  it 

\^jj  inches  \  the  line  that  is  left  is  ■ and  

tenths  inches  long.     3  —  IfV  = 

8.  William  drew  a  square.  Each  side  of  it  was 
ly^  inches.     We  might  call  it  a  ly^-inch  square. 

The  perimeter  of  the  square  was  — —  and  

inches.     ly\j-  x  4  = 

9.  Egbert  had  a  piece  of  copper  wire  1-|-  inches 
long.  He  divided  it  into  pieces  each  of  which  was 
y^Q    of    an    inch   long.      There   were  pieces. 

-■-2      •      10 

10.  Herbert  had  a  piece  of  silver  wire  1.2  inches 
long.  He  divided  it  into  3  equal  parts.  Each 
part  was  ■ of  an  inch  long.     1.2  in.  ^ 


3  =          lA  in.  - 

3  = 

Copy  and  add: 

35|             515 

617 

714 

81.4 

24y^            607 

505 

408 

30.8 

PART  II,  107 

12  sixes  are  72  11  sixes  are  G6 

6  twelves  are  72         6  elevens  are  66 

1.  Can  you  add  column  (a)  in  fifteen  seconds, 
beginning  at  the  top?                         abode 

6     2  4  6  6 

2.  Can  you  add  column  (a)       q     q  q  q  2 

in  fifteen  seconds,  beginning  at       6     6  6  6  1 

the  bottom?                                       6     6  6  5  3 

6     6  6  6  5 

3 .  Practice  until  you  can  do       6     6  6  6  4 

this  with  each  column.                      6     6  6  6  6 

6     6  6  4  3 

4.  Ten  sixes  are  .                6     6  6  6  2 

5.  Eleven  sixes  are  .           6     6  6  6  5 

6.  Twelve  sixes  are  .          b     b  b  6  1 

7.  Twenty  sixes  are  .          n     n  r^  ^  t 

0       0  D  D  0 

8.  27  +  6=          37  +  6=         6     6  6  6  1 

9.  17  +  6=          47  +  6=         I     t  ^c  t  t 
10.  87  +  6=          67  +  6=         6     6  6  2  3 


11.  86  +  6=  46  +  6  = 

12.  36  +  6=  56  +  6  = 


1  J  J     6     2 
6 


3 

13.  16  +  6=  26  +  6=  1 

2 

14.  48  +  6  =  58  +  6  =       18  +  6  =  5 

15.  28  +  6  =  38  +  6  =       68  +  6  =  4 

_3 

Copy  and  subtract: 

48-1,      423      532      643      75.2 
23tV      165  .    196      286      28.6 


108 


ELEMENTARY    ARITHMETIC. 


1.  2  is  contained  in  11  - 

2.  2  is  contained  in  11  - 

3.  3  is  contained  in  13  - 

4.  3  is  contained  in  13  - 

5.  3  is  contained  in  11  - 

6.  3  is  contained  in  11  - 

7.  3  is  contained  in  14  - 
8o  3  is  contained  in  14  - 

9.  4  is  contained  in  17  - 

10.  4  is  contained  in  17  - 

11.  4  is  contained  in  19  - 

12.  4  is  contained  in  19  - 

13.  5  is  contained  in  22  - 

14.  5  is  contained  in  22  - 

15.  5  is  contained  in  33  - 

16.  5  is  contained  in  33  - 

17.  5  is  contained  in  42  - 

18.  5  is  contained  in  42  - 

19.  21  is  —    5's  and  — . 

20.  23  is  —  lO's-and  — . 

21.  22  is  —    7's  and  — . 

22.  24  is  —    7's  and  — . 


Copy  and  multiply: 

44  46 

^2  ^2 


26 
2i 


times  and 
and - 

times  and 
and - 


times  and 
and - 

times  and 
and - 


times  and 
and 


times  and 
and 


times  and 
and - 


times  and 
and - 


-  over, 
times. 


over. 


times. 


over. 


times. 


over. 


times. 


over. 


times. 


over. 


times. 


over. 


times. 


over. 


-   times. 

-  times  and  ■ — -  over. 

-  and times. 

22  is  —  4's  and  — . 
21  is  —  2's  and  — . 

23  is  —  3's  and  — . 

24  is  —  8's. 


64 


n 


24 

2i 


PART    II.  109 

1.  20  ft.  +  17  ft.,  means . 

20  ft.  and  IT  ft.  - 

2.  20  ft.  -  17  ft.,  means . 

20  ft.  less  ITft.  = 

3.  20  ft.  X  2,  means .     2  times . 

4.  20  ft.  X  2^,  means .    2^  times . 

5.  20  ft.  -^  4  ft.,  means . 

4  ft.  are  contained  . 

6.  20  ft.  -^  4,  means .     i  of  . 


7.  4^  ft.  +  4-  ft.,  means .     i^  ft.  and  ^  ft. 

8.  ^  it.  —  ^  ft.,  means .     ^  ft.  less  ^  ft. 

9.  2  J-  ft.  X  4,  means .     4  times  

10.  4-  ft.  X  24-,  means .    24  times 

11.  |-  ft.  -=-  f  ft.,  means . 

f  ft.  are  contained  

12.  64  ft.  ^  3,  means .     ^  of  — . 


13.  .8  in.  +  .4  in.,  means 

.8  in.  and  .4  in.  = 

14.  1.2  in.  —  .5  in.,  means 


1.2  in.  less  .5  in.  = 

15.  1.2  in.  X  3,  means ■.    3  times  — 

16.  1.2  in.  X  24,  means .    2^  times 

17.  1.6  in.  ^  .4  in.,  means . 

.4  in.  are  contained  — 


18    1.6  in.  ~  4,  means .     4-  of . 

Copy  and  divide: 

$5)$525   $5)$515   $5)$1025   $5)$1015 


110  ELEMENTARY    AIUTHMETIC. 

Thirty  days  liatli  September, 

April,  June,  and  November. 
Each  of  the  other  months  has  31  days,  except  February. 
February  has  29  days  in  a  leap-year  and  28  days  in  all 
other  years. 

THIS    YEAR. 

1.  In  January  there  are  —  weeks  and  —  days. 

2.  In  February  there  are  —  weeks  and  — . 

3.  In  March  there  are  —  weeks  and  —  days. 

4.  In  April  there  are  —  weeks  and  —  days. 

5.  In  May  there  are  —  weeks  and  —  days. 

6.  In  June  there  are  —  weeks  and  —  days. 

7.  In  July  there  are  —  weeks  and  —  days. 

8.  In  August  there  are  —  weeks  and  —  days. 

9.  In  September  there  are  —  weeks   and  — 
days. 

10.  In  October  there  are  — -  weeks  and  —  days. 

11.  In  November  there  are  —  weeks  and  — 
days. 

12.  In  December  there  are  —  weeks  and  — 
days. 

Can  you  read  the  12  statements  given  above, 
filling  each  blank  correctly,  in  40  seconds?  Can 
you  do  it  if  they  are  put  ujoon  the  blackboard  in 
some  other  order?     Try  it. 

13.  In  February,  1896,  there  were  —  weeks 
and  —  day. 

Copy  and  divide : 

5)$525    5)$515    5)$1025    5)$1015 


PART   II. 


Ill 


4  sevens  are  28 
7  f  oui-s  are  28 
4  eights  are  32 


5  sixes  are  30 

6  fives  are  30 
8  fours  are  32 


1.  Thirty-two  pecks  are  — 

2.  Twenty-four  quarts  are 

3.  Twenty-eight  days  are 


bushels. 

—  pecks. 

—  weeks. 

—  wholes. 


4.  Twenty-eight  fourths  are  — 

5.  Thirty  fifths  are  wholes. 

6.  7  bushels  are  pecks.     6  bushels  = 

7.  4  weeks  are  days.         3  weeks  = 

8.  10  yards  are  feet.         9  yards  = 

9.  Thirty  inches  are feet  and inches. 

10.  Thirty  days  are  weeks  and days. 

gallons  and . 

dollars  and . 

bushels    and 


1 1 .  Thirty-one  quarts  are  — 

12.  Thirty-two  dimes  are  — 

13.  Thirty-three    pecks    are 


14.  Thirty-four  quarts  are 


pecks  and 


15.  Four  weeks  and  3  days  are 

16.  Ten  yards  and  2  feet  are  — 


—  days. 

-  feet. 

17.  Seven  bushels  and  3  pecks  are  pecks 

18.  Two  feet  and  8  inches  are  inches. 

19.  Four  pecks  and  1  quart  are  quarts. 


20.  Six  gallons  and  3  quarts  are 


quarts 


Copy  and  add: 

24|      345 

138 

224 

27.3 

33      226 

304 

246 

30.2 

25A     216 

225 

108 

35.9 

112  ELEMENTARY    ARITHMETIC. 

1.  The  sum  of  $12  and  $4  is  — —  dollars. 

(a)  Find  the  sum  of  $84  and  $43.* 

2.  The  difference  of  $12  and  $4  is dollars. 

(b)  Find  the  difference  of  $85  and  $42. 

There  can  he  no  product  of  $8  and  $^. 

3.  The  product  of  $8  and  4  is  dollars. 

(c)  Find  the  product  of  $82  and  4. 

4.  The  quotient  of  $28  divided  by  $7  is  , 

(d)  Find  the  quotient  of  $628  divided  by  $2. 

5.  The  quotient  of  $28  divided  by  7  is  . 

(e)  Find  the  quotient  of  $628  divided  by  2. 

6.  A  lady  bought  4  yards  of  gingham  at  8^  a 
yard;  she  gave  the  salesman  half  a  dollar;  she 
should  receive  in  change  cents. 

7.  A  man  paid  $8  for  a  watch;  he  paid  $4  for 
repairing  it;  he  then  sold  the  watch  for  $15;  he 
gained  dollars. 

8.  Alice  paid  8^  for  pens,  5^  for  a  pencil  and 
5^  for  paper.  If  she  gave  the  salesman  1  fourth 
of  a  dollar,  how  much  change  should  she  receive? 
She  should  receive  . 

9 .  Peter  had  half  a  dollar ;  he  spent  1  tenth  of 
a  dollar;  he  had  cents  left. 


Copy  and  subtract: 

53|             504 

603 

705 

70.5 

21t-V           268 

377 

489 

48.9 

*  Problems  designated  by  letters  are  for  the  slate. 


PART    II.  113 

1.  If  I  should  draw  an  oblong  4  inches  wide 
and  8  inches  long  and  then  divide  it  into  1-inch 

squares,  there  Avould  be  rows  of  squares  and 

in  each  row  there  would  be  squares. 

2.  The  area  of  an  oblong  4  inches  by  8  inches 
is  square  inches. 

3.  The  perimeter  of  an  oblong  8  inches  by  4 
inches  is  inches. 

4.  The  first  day  of  August,  1895,  was  Thurs- 
day;   the  next  Thursday  was  the    th;    the 

ninth  was  ;  the  seventh  was  . 

5.  Eight  4-cent  stamps  cost  cents. 

6.  At  5^  a  quart,  6  quarts  of  milk  cost  

cents;  5  quarts  cost  cents. 

7.  At  4^  a  quart,  7  quarts  of  milk  cost  

cents;  8^  quarts  cost  cents. 

8.  A  man  agreed  to  pay  $4  a  day  for  keeping 
his  family  at  a  hotel.  One  week's  board  will  cost 
dollars. 

9.  It  takes  5  minutes  for  Alice  to  go  home 
from  school ;  Mary  lives  farther  away,  and  it  takes 

her  six  times  as  long ;  it  takes  Mary  • minutes 

to  go  home  from  school.     Alice  and  Mary  started 

for  home  at  3:15 ;  Alice  reached  home  at : 

Mary  reached  home  at — ■. 

Copy  and  multiply : 

56  74  98  58  76 

2i  2i  2i  2i  2i 


114  ELEMENTARY    ARITHMETIC. 


1. 

3  bu.  2  pk.  +  4  bu. 

1  pk.  = 

3i  +  4]. 

2. 

4  bu.  3  pk.  -  2 

bu. 

2  pk.  = 

4|  -  2-^ 

3. 

5  biT.  1  pk.  X  3 

= 

51x3 

4. 

2  bu.  2  pk.  X  2, 

L  _ 

2^x2^ 

5. 

2  bu.  2  pk.  -  2 

pk. 

— 

2i^    i 

6. 

2  pk.  -  4  = 

1^4 

7. 

$2.4  + $3.1  =r 

2i+3/„ 

8. 

$6.8-  $3.1=. 

H  -  3tV 

9. 

$5.2  X  4  = 

51x4 

10. 

$4.2  X  2\^ 

41x2^ 

11. 

$3.6-  $.6  = 

3|^   1 

12. 

$3.6-3  = 

3f-3 

13.  The  long  hand  of  a  clock  moves  from  X  to 

XII  in   mmutes;    from  YI  to   X  in  

minutes. 

14.  The  short  hand  of  a  clock  moves  from  IX 
to  XI  in ;    from  IV  to  VIII  in  


15.  The  best  trains  go  from  Waukegan  to  Chi- 
cago in  50  minutes ;  such  a  train  leaving  Wauke- 
gan at  10:30  should  arrive  in  Chicago  at  . 

16.  A  train  from  Aurora  was  due  in  Chicago  at 
2:15;  it  arrived  at  2:45;  it  was minutes  late. 

17.  From  1:30  to  2:45  it  is hour  and 

minutes. 

Copy  and  divide: 

$5)$630   .  $5)$620   ■  $5)$610    $5)|640 


PART    II, 


115 


1.  One  third  is  

2.  One  sixth  is  — - 

3.  Two  thirds  are  - 

4.  Two  sixths  are  - 

5.  Tliree  sixths  are 


twelfths, 
twelfths. 

—  twelfths. 

—  twelfths. 

twelfths. 


6. 
7. 
8. 
9. 
10. 


One  third  and  1  twelfth  are 
One  third  less  1  twelfth  are 
One  sixth  and  1  twelfth  are 
One  sixth  less  1  twelfth  is  - 


Five  sixths  and  1  twelfth  are 

1 1 .  Five  sixths  less  1  twelfth  are 

1 2 .  Seven  twelfths  and  1  sixth  are 

1 3 .  Seven  twelfths  and  1  third  are 

14.  Two  times  5  twelfths  are  — 

15.  Three  times  5  twelfths  are  — 


—  twelfths. 
— ■  twelfths. 

—  twelfths, 
twelfth. 

—  twelfths. 

—  twelfths. 

—  twelfths. 

—  twelfths, 
twelfths. 


16.  Two  twelfths  are  contained  in  1  half 

times. 

17.  Two   twelfths    are    contained    in    1    whole 


18.  One  half  of  1  sixth  is  — 

19.  One  fourth  of  1  third  is 


Copy  and  divide : 

5)$6P>0  5)$62Q 


5)$610 


5)$640 


116  ELEMENTARY   ARITHMETIC. 

1.  One  inch  is of  a  foot. 

2.  Two  inches  are  of  a  foot. 

3.  Three  inches  are of  a  foot. 

4.  Four  inches  are  of  a  foot. 

5.  Five  inches  are of  a  foot. 

6.  Six  inches  are of  a  foot. 

7.  Seven  inches  are of  a  foot. 

8.  Eight  inches  are —  of  a  foot. 

9.  Nine  inches  are of  a  foot. 

10.  Ten  inches  are of  a  foot. 

11.  I  of  a  ft.  +  tV  of  a  ft.  =  3|  +  3yV  -= 

12.  4  of  a  ft.  -  yV  of  a  ft.  =  4|  -  2^V  = 

13.  ^\  of  a  ft.  X  2  =  6-j-V  X  2  =: 

14.  Hft.-|ofaft.=  1|^tV- 

15.  6|ft. -2=  61-4-2  = 

16.  Draw  a  line  3^  ft.  long;  draw  another  line 

4y^^  ft.  long ;  together  the  lines  are and  — — 

feet  long.     3|-f  4^^  = 

17.  Draw  a  line  3  ft.  long;  erase  from  it  ly^-g- 

feet;  the  line  that  is  left  is  and 

feet  long.     3  —  lyV  — 

18.  Henry  drew  a  1^-foot  square.     The  perim- 
eter of  the  square  was  


240 
175 


Copy 

and  add: 

35| 

352 

23 

143 

35A 

262 

l|x4  = 

302 

45.3 

184 

30.1 

231 

25.2 

PART   II.  117 

12  sevens  are  84  11  sevens  are  77 

7  twelves  are  84  7  elevens  are  77 

1.  Can  you  add  column  (a)  in  fifteen  seconds, 
beginning  at  the  top? 

2.  Can  you  add  column  (a)       ^     o      a  n     ^ 
in  fifteen  seconds,  beginning  at       7     7     7  7     2 

the  bottom?                                       7     7     7  7     1 

3 .  Practice  until  you  can  do       7     7     7  7     4 
this  with  each  cohimn.                       7     7     7  7     6 

7     7     7  7     3 

4.  Ten  sevens  are  .             7     7     7  7     4 

5.  Eleven  sevens  are  .        7     7     7  7     2 

6.  Twelve  sevens  are  .       7     7     7  7     5 

7.  Twenty  sevens  are  .        (     1     (  7     o 

^  11111 

8.  27  +  7  =         17  +  7  =        7     7     7  7     G 

9.  37  +  7=         57  +  7=        7     7     7  7     1 

7     7     7  7     4 

10.  46  +  7  =         16  +  7  =       J:  J  _^  _I     ^ 

11.  26  +  7  =         56  +  7  =  2 

12.  38  +  7  =         18  +  7  =  '> 

13.  48  +  7  =         28  +  7  =  "^ 

4 

14.  25  +  7  =         15  +  7  =        35  +  7  =  6 

15.  65  +  7  =         45  +  7  =        75  +  7  =  A 

Copy  and  subtract; 

65 1      640     560     470  38 

32^V     236      345      134  14.6 


118 


ELEMENTARY    ARITHMETIC. 


1.  5  is  contained  in  11  times  and 

2.  5  is  contained  in  11  — -  and - 

3.  5  is  contained  in  12 times  and 

4.  5  is  contained  in  12  — -  and - 

5.  5  is  contained  in  13  - 

6.  5  is  contained  in  13  - 

7.  5  is  contained  in  14  - 

8.  5  is  contained  in  23  - 


times  and 

and - 

and - 

and - 


9.  5  is  contained  in  28  — -  and 

10.  5  is  contained  in  33 and 

11.  5  is  contained  in  37 and 

12.  5  is  contained  in  41 and 

13.  5  is  contained  in  48 and 


-  over, 
times. 


over. 


times. 


over. 


times, 
times, 
times. 

times, 
times, 
times, 
times, 
times. 


14.  When  milk  costs  2^  a  pint,  for  7^  I  can  buy 
—  and pints.     7^  ^  2^  — 


15.  When  ribbon  costs  3^  a  yard,  for  10^  I  can 
buy  and  yards.     10^  -^  3^  = 

16.  When  milk  is  4^  a  quart,  for  10^  I  can  buy 
— —  and ■  quarts.     10^  -^  4^  = 


30  is 


17. 
18. 

19.  32  is 


30  is 


7's  and 
4's  and 
5's  and 


30  is 


31  is 

32  is 


9's  and  - — . 
G's  and  — . 
3's  and  — . 


Copy  and  multiply 

28       38 


91 

^2 


2i 


48 
2i 


68 


78 
24 


PART  II.  119 


1.  30  mill.  +  15  mill.,  means  

30  min.  and  15  min. 

2.  30  min.  —  15  min.,  means 


30  min.  less  15  min.  = 

3.  12  min.  x  2,  means .     2  times  — 

4.  12  min.  x  2 J,  means .     2h  times 

5.  30  min.  -^  5  min.,  means . 

5  min.  are  contained 

6.  30  min.  ^  5,  means .      4-  of 


7.  4-  ft.  +  -f'Y  ft.,  means  . 

-I-  ft.  and  -iV  ft.  = 

8.  |-  ft.  —  -j^  ft.,  means  . 

^  I  ft.  less  3-V  ft-  = 

9.  3y^-2-  ft.  X  5,  means .       5  times  — 

10.  6  ft.  X  2-|-,  means .       2|-  times  — 

11 .  2yV  ft.  -^  3^  ft.,  means .    yV  ft.  is 

12.  8|  ft.  ^  2,  means .     I  of 


13.  $.7  +  $.5,  means  • .     $.7  and  $.5  = 

"  14.  $1.5  -  $.8,  means .     $1.5  less  $.8  = 

15.  $1.2  X  4,  means .      4  times . 

16.  $.6  X  2|,  means  ■ .    2h  times  — . 

17.  $2.4  -  $.6,  means -.     $.6  are . 

18.  $2.4  -  6,  means .     |  of . 

19.  From  9:10  to  9:35  it  is  minutes. 

20.  From  9:50  to  10:10  it  is  minutes. 

Copy  and  divide: 

21b.)451b.     21b.)631b.    21b.)871b.     21b.)291b. 


120  ELEMENTARY    ARITHMETIC. 


1.  What  day  of  the  week  is  it?     To-day  is 

.       Two    weeks    from    to-day    will    be 

.       Four    weeks    from    to-day    will    be 

Four  weeks  and  1  day  from  to-day 


will  be  .     Twenty-nine  days  from  to-day 

will  be  .     Thirty  days  from  to-day  will 

be  .     Four  weeks  and  three  days  from 

to-day  will  be  .     Thirty-one  days  from 

to-day  will  be  . 

2.  From    January    1st  to    February   1st  it   is 

days. 

From  February  1st  to  March  1st  it  is  

days. 

From  March  1st  to  April  1st  it  is days. 

From  April  1st  to  May  1st  it  is  days. 

From  May  1st  to  June  1st  it  is  days. 

3.  The  year  1896  Avas  a  leap-year.     February, 
1896,  had  days. 

4.  January  1st,  1896,  was  Wednesday;  Febru- 
ary 1st,  1896,  was  . 

5.  August  1st,  1896,  was  Saturday;  September 
1st,  1896,  was  . 

6.  February  1st,  1896,  w^as  Saturday;  March 
1st,  1896,  was  . 

7.  September  1st,  1896,  was  Tuesday;  October 
1st,  1896,  was  . 

Copy  and  divide: 

2)45  lb.  2)63  lb.  2)87  lb.  2)29  lb. 


PART  II. 


121 


5  sevens  are  35         4  nines  are  36 
7  fives  are  35  9  fours  are  36 

6  sixes  are  36 


1.  Thirty-six  pecks  are  

2.  Thirty-five  days  are  

3.  Thirty-six  spoons  are  

4.  Thirty-five  fifths  are  

5.  Thirty-six  ninths  are  

6.  9  gallons  are  quarts. 

7.  5  weeks  are  days. 

8.  Thirty-seven  inches  are  — 

9.  Thirty-eight  days  are 

10.  Thirty-nine    quarts    are   - 


bushels, 
weeks. 

-  sets. 
wholes, 
wholes. 

8  gallons 
4  weeks  = 

—  feet  and  - 
weeks  and  - 


11.  Five  weeks  and  2  days  are  - 

12.  Three  feet  and  3  inches  are 

13.  Nine  bushels  and  1  peck  are 


gallons   and 


days, 
inches. 
-  pecks. 


14.  2|  are 

15.  2|-  are 

16.  2f  are 

17.  2|-  are 

18.  li  are 

19.  41  are 


thirds. 

fourths. 

fifths. 

fifths. 

thirds, 


3 1  are 
3|-  are 


31-  are 


3|-  are 
4|  are 


tiiirus.      '±f  ctru 

fourths.  4|-  are 


thirds. 

fourths. 

fifths. 

fifths. 

thirds. 

fourths. 


Copy  and  add: 

304 
240 


32| 
23 


158 


425 
106 
232 


356 
114 
205 


24.T 
10.2 
33.4 


122  ELEMENTARY    ARITHMETIC. 

1.  Add  6  bu.,  4  bu.,  2  bu.,  and  1  bu. 

(a)  Add  344  bu.,  46  bu.,  and  35  bu. 

2.  From  19  bushels  subtract  6  bushels. 

(b)  From  472  bushels  subtract  146  bushels. 

3.  Multiply  9  bushels  by  4. 

(c)  Multiply  292  bushels  by  3. 

4.  Divide  35  bushels  by  5  bushels. 

(d)  Divide  525  bushels  by  5  bushels. 

5.  Divide  35  bushels  by  5. 

(e)  Divide  525  bushels  by  5. 

6.  At  $3  a  barrel,  8  barrels  of  apples  cost . 

(f)  At  $236  an  acre,  2  acres  of  land  cost . 

7.  Two  thirds  of  12  dollars  are  dollars. 

(g)  Two  thirds  of  99  dollars  are  ■ dollars. 

(h)  Two  thirds  of  96  dollars  are  dollars. 

8.  Twelve  dollars  are  f  of  dollars. 

(i)  Forty-four  dollars  are  f  of  dollars. 

(j)  Forty-six  dollars  are  f  of  dollars. 

9.  A  lady  bought  8  yards  of  lace  at  $2  a  yard; 
she  gave  the  salesman  two   ten-dollar  bills;    she 


o±xijLi±*^   icv^cxvv::;   xxx   v^jlxc 

Aji-l^K. 

K.\.KJ±±(Aji.O. 

Copy  and  subtract: 

461             475 

565 

455 

35.5 

23^^           235 

236 

237 

12.8 

PART  II.  123 

1.  Tliink  of  an  oblong  5  inches  by  7  inches. 
Think  of  it  divided  into  1-inch  squares.  The  area 
of  the  oblong  is square  inches. 

2.  The  perimeter  of  an  oblong  5  inches  by  7 
inches  is  inches. 

3.  The  first  day  of  September,  1895,  was  Sun- 
day ;  the  second  Sunday  was  the th ;  the  third 

Sunday  was  the  ;  the  fourth  Sunday  was  the 

;  the  fifth  Sunday  was  the  . 

4.  The  first  Sunday  of  August,  1895,  was  the 
fourth  day  of  the  month;  the  second  Sunday  was 

the  th;   the  third   Sunday  was  the  th; 

the  fourth  Sunday  was  the  th. 

5.  The  Saturdays  of  August,  1895,  were  the 
3d,  ,  ,  ,  and  . 

6.  A  passenger  train  runs  from  Waukegan  to 
Lake  Forest  in  15  minutes.  If  the  train  leaves 
Waukegan  at  9:50  it  should  reach  Lake  Forest  at 


7.  John  rode  32  miles  in  4  hours;  he  rode  at 

the  rate  of  miles  an  hour.     32  miles  -^ 

4  = 

8.  Henry  rode  33  miles  in  4  hours;  he  rode  at 

the  rate  of  miles  an  hour.     33  miles  -^- 

4  = 


Copy  and  multiply : 

45                65 

85 

25 

47 

2i                2i 

24 

2i 

24 

124  ELEMENTARY    ARITHMETIC. 

1.  3  ft.  6.  in.  +  3  ft.  7  in.  =         3|  +  3^^-^  = 

2.  3  ft.  6  in.  -  1  ft.  4  in.  =         ^  -  1^    = 

3.  4  ft.  8  in.  X  4  ==  4|  x  4      = 

4.  4  ft.  6  in.  -f-  6  in.  =  4|  -    I    = 

5.  4  ft.  6  in.  -  2  =  4|  -  2      = 

6.  The  letters  A.M.  stand  for  the  words  ante 
meridiem.     These  words  mean  before  noon. 

7.  The  letters  P.M.  stand  for  the  words  post 
meridiem.     These  words  mean  after  noon. 

8.  From  10  o'clock  A.M.  to  2  o'clock  P.M.  it 
is  hours. 

9.  From  9  o'clock  P.M.  to  4  o'clock  A.M.  it 
is  hours. 

10.  From  4:30  P.M.  to  6:30  P.M.  it  is  . 

11.  Mr.  Smith  begins  work  at  7  o'clock  A.M.; 
he  has  one  hour  for  dinner  and  rest  at  noon,  and 
then  works  until  6  o'clock  P.M.  Each  day  he 
works  hours. 

12.  A  train  from  Chicago  was  due  in  Waukegan 

at  10:45;  it  arrived  at  11:10;  it  was minutes 

late. 

13.  A  tram  moved  30  miles  in  1  hour;  this  was 
at  the  rate  of  1  mile  in  minutes. 

14.  A  train  moved  at  the  rate  of  40  miles  an 

hour  for  2  hours  and  30  minutes;  it  moved  

miles. 

Copy  and  divide : 

31b.)671b.     3  lb.)97  lb.     31b.)371b.    3  lb.)38  lb. 


PART    II. 


125 


1.  One  third  is  

2.  One  fourth  is  

3.  Two  thirds  are  — 

4.  Three  fourths  are 


twelfths. 

-  twelfths. 

-  twelfths. 

twelfths. 


5.  Add  1  fourth  and  1  third. 

1  fourth  is  twelfths. 

1  third  is  twelfths. 

—  twelfths  and twelfths  are 


twelfths. 


6.  Add  2  thirds  and  1  fourth. 

2  thirds  are  twelfths. 

1  fourth  is  twelfths. 

—  twelfths  and twelfths  are 


twelfths. 


7. 


From  3  fourths  subtract  1  third. 

3  fourths  are  twelfths. 

1  third  is  twelfths. 

twelfths  less twelfths  are  — 


8.  One  fourth  of  a  foot  and 
are  twelfths  of  a  foot. 


twelfths. 


1  third  of  a  foot 


Copy  and  divide: 

3)67  lb.  3)97  lb. 

—  lb. 


3)37  lb. 


3)38  lb. 


1 

"3 

+ 

1  _ 

1 
T 

— 

1  _ 

1 

X 

6  = 

1 
"3 

X 

6i  = 

1 
"5 

-^ 

1   _ 

1  2    - 

1 
3 

-^ 

4  = 

126  ELEMENTARY    ARITHMETIC. 

1 .  4  of  a  dozen  +  4-  of  a  dozen  = 

2.  1^  of  a  dozen  —  4-  of  a  dozen  = 

3.  ^  of  a  dozen  x  6  = 

4.  I  of  a  dozen  x  6^^  = 

5 .  I  of  a  dozen  -^  -j^  of  a  dozen  := 

6.  \  oi  2i  dozen  -=-  4  = 

7.  Draw  a  line  2|  feet  long;  draw  another  line 
2^  feet  long ;  together  the  lines  are and 

feet  long.     2|  +  2|  = 

8.  Draw  a  line  4  feet  long;  erase  from  it  IfV 

f eet ;  the  line  that  is  left  is  and 

feet  long.     4  —  1^^  = 

9.  James  drew  a  square.  Each  side  of  it  was 
1^  feet  long.  We  might  call  it  a  ly-^-foot  square. 
The  perimeter  of  the  square  was  and  

feet.     lyV  X  4  = 


10.  Peter  had  a  piece  of  copper  wire  \\  feet 
long.  He  divided  it  into  j^ieces,  each  of  which  was 
-f  of  a  foot  long.    There  were pieces.    1-^ 


X  — 

6  ~ 


11.  Harry  had  a  piece  of  silver  wire  1|  feet 
long.  He  divided  it  into  2  equal  pieces.  Each 
piece  was  ■ of  a  foot  long.     \l  ^2  = 


12.  l|feet-- 

1 

of 

a  foot  = 

1|  feet  -f 

2  = 

13.  14- feet - 

1 
T 

of 

a  foot  — 

14-  feet  -f 

-2  = 

Copy  and  add: 

43|-              414 

524 

335 

31.6 

22                306 

207 

407 

41.6 

31A            412 

623 

502 

51 .6 

PART  II.  127 

12  eights  are  96         11  eights  are  88 
8  tAvelves  are  96         8  elevens  are  88 

1.  Can  you  add  column  (a)  in  fifteen  seconds, 
beginning  at  the  toj)? 

a     b  c  d  e 

2.  Can  you  add  column  (a)        o     o  a  n  o 

in  fifteen  seconds,  beginning  at       8     8  8  8  2 

the  bottom?                                       8     8  8  8  7 

8     8  8  8  6 

3 .  Practice  until  you  can  do       8     8  8  8  3 

this  with  each  column.                      8     8  8  8  5 

8     8  8  8  1 

4.  Ten  eights  are  .             8     8  8  8  4 

5.  Eleven  eights  are  .         8     8  8  8  8 

6.  Twelve  eights  are  .       8     8  8  8  6 

7.  Twenty  eights  are  . 


8     8     8     8     2 
8     8     8     8     7 


8.  27  +  8  =         17  +  8  =         8     8     8     8     3 

9.  37  +  8  =         57  +  8  =         13     5     7     4 

5 

10.  46  +  8  =         16  +  8  =  2 

11.  26  +  8=         56  +  8=  1 

8 

12.  38  +  8=         18  +  8=         58  +  8=  2 

13.  48  +  8  =         28  +  8  =-        78  +  8  =         6 

7 

14.  25  +  8  =         15  +  8  =        35  +  8  =       _5 

15.  65  +  8  =         55  +  8  =        75  +  8  = 

Copy  and  subtract: 

48 1-      444     554     464     47.4 
26^V     125      126      127      12.8 


128 


ELEMENTARY    ARITHMETIC. 


1.  6  is  contained  in  13 times  and 

2.  6  is  contained  in  13  — -  and - 

3.  6  is  contained  in  14  times  and 

4.  6  is  contained  in  14 and - 


-  over, 
times. 


over. 


5.  6  is  contained  in  15 

6.  6  is  contained  in  15 

7.  6  is  contained  in  1 6 

8.  6  is  contained  in  16 

9.  6  is  contained  in  17 
10.  6  is  contained  in  IT 


times  and 
and - 

times  and 
and - 

times  and 
and - 


times. 


over. 


times. 


over 


times. 


over. 


11.  6  is  contained  in  25 and 

12.  6  is  contained  in  20 and 

13.  6  is  contained  in  34 and 


times. 

times, 
times, 
times. 


14.  When  milk  costs  6^  a  quart,  for  27^  I  can 
buy  and quarts.     27^  ^  6^  = 

15.  If  books  cost  6^  each,  with  27^  I  can  buy 
— —  books  and  have cents  left.     27^  -^  6^  = 


16.  When  milk  costs  6^  a  quart,  for  33^  I  can 
buy  and quarts.     33^  -^  6^  = 

17.  If  books  cost  6^  each,  with  33^  I  can  buy 
books  and  have cents  left.     33^  -^  6^  = 


Copy  and  multiply : 

36                39 

33 

63 

66 

2i                2i 

2i 

2i 

24 

PART  II.  129 

1.  $.8  +  $.6,  means  .       $.8  and  $.6  =: 

2.  $1.6  -  $.9,  means  .  $1.6  less  $.9  -= 

3.  $1.5  X  4,  means  .  4  times  $1.5  = 

4.  $.8  X  21,  means  .  24- times  . 

5.  $2.4  -  $.8,  means  .  $.8  are  -. 

6.  $2.4  -  8,  means .    |  of 


7.  I  can  change  fourths  to  8ths,  to  ,  to 


8.  One  fourth  is  twentieths.     -^  is  

twenty-fourths.     4-  is  thirty-seconds. 

9.  I  can  change   fifths  to  lOths,  to  ,  to 


? 


10.  One  fifth  is  twenty-fifths.     4"  i^  

thirtieths,     f  are  twenty-fifths. 

11.  George  had  a  quarter  of  a  dollar;  he  spent 
1  tenth  of  a  dollar;  he  had  cents  left. 

12.  Richard  played  ball  half  an  hour,  and  he 
played  "hide  and  seek"  10  minutes;  in  all  he 
played  minutes. 

13.  Helen  practiced  her  music  lesson  from  7:30 
to  8:45;  she  practiced  hour  and  min- 
utes. 

14.  34  are  halves.         44  are . 


2"   ctxc  ixciavco.  -i^ 

15.  3|  are  thirds.    '      4^  are  . 

16.  3|-  are  fourths.       4|  are  . 

17.  3i  are  fifths.  4|-  are . 

Copy  and  divide: 
3qt.)64qt.    3  qt.)65  qt.    3  qt.)94  qt.    3  qt.)95  qt. 


130  ELEMENTARY    ARITHMETIC, 


1.  What   day   of   the  week  is  it?     To-day  is 
Fourteen  days  from  to-day  will  be 


Fifteen  days  from  to-day  will  be  .     Thirteen 

days  from  to-day  will  be  . 

2.  January  1st,  1898,  was  Saturday;  February 

1st  was  ;    March  1st  was    ;    April   1st 

was  . 

3.  John  lives  2  miles  from  the  schoolhouse; 
Peter  lives  1  and  3  tenths  miles  from  the  school- 
house.  How  much  farther  is  John's  home  from 
the  schoolhouse  than  Peter's?     It  is  . 

4.  Harvey  rode  on  his  bicycle  2  and  3  tenths 
miles:    Ernest  rode  3  times  as  far;   Ernest  rode 


5.  One  fourth  of  12.8  miles  is  . 

6.  Three  fourths  of  12.8  miles  are  ^ . 

7.  Twelve  and  4  tenths  miles  are  two  thirds  of 
miles. 


8.  Twelve  and  4  tenths  miles  are  one  half  of 
miles. 


9.  I  am  thinking  of  an  oblong  whose  area  is 

12  square  inches.     It  is  6  inches  long.     It  is  

inches  wide. 

10.  I  am  thinking-  of  an  oblong  whose  area  is 

15  square  inches.     It  is  5  inches  long.     It  is  

inches  wide. 

Copy  and  divide : 
3)64  qt.  3)65  qt.  3)94  qt.  3)95  qt. 


PART   II.  131 

5  eights  are  40         6  sevens  are  42 
8  fives  are  40  7  sixes  are  42 

5  nines  are  45  9  fives  are  45 

1.  Forty  quarts  are  pecks. 

2.  Forty-two  days  are  weeks. 

3.  Forty-two  spoons  are  sets. 

4.  Forty-five  ninths  are  wholes. 

5.  10  gallons  are  quarts.     9  gallons  = 

6.  6  weeks  are  days.  5  weeks  = 

7.  Forty  inches  are  feet  and  . 


8.  Forty-five  days  are  weeks  and  . 

9.  Forty-six  quarts  are gallons  and 

10.  Six  weeks  and  4  days  are  days. 

11.  Three  feet  and  7  inches  are  inches. 

12.  Eleven  bushels  and  1  peck  are  pecks. 

13.  2|  are  sixths.     3|  are  sixths. 

14.  4|  are  sixths.     5|  are  sixths. 

Read  first  by  column,  then  by  line. 

3  2's  are .     3  3's  are .     3  4's  are 

3  5's  are .     3  6's  are .     3.  7's  are 

3  8's  are .     3  9's  are .     3  lO's  are 


Copy  and  add: 

53i              522  431  353  48.2 

21                643  603  505  30.3 

521              281  294  661  42.1 


132  ELEMENTARY    ARITHMETIC. 

1.  Add  2  ft.  10  in.  and  4  ft.  5  in. 

(a)  Add  146  ft.  10  in.  and  83  ft.  6  in. 

2.  From  16  subtract  the  sum  of  4  and  8. 

(b)  From  256  subtract  the  sum  of  47  and  38. 

3.  Multiply  2  ft.  3  in.  by  5. 

(c)  Multiply  53  ft.  4  in.  by  5. 

4.  Divide  42  feet  by  6  feet. 

(d)  Divide  444  feet  by  6  feet. 

5.  Divide  42  feet  by  6. 

(e)  Divide  444  feet  by  6. 

6.  At  $5  a  ton,  9  tons  of  coal  cost  . 

(f)  At  $125  each  J  3  horses  cost  . 

7.  Three  fourths  of  12  dollars  are dollars. 

(g)  Three  fourths  of  120  dollars  are dollars. 

8.  Twelve  dollars  are  |  of  dollars. 

(h)  One  hundred  and  twenty  dollars  are  f  of 
dollars. 


9.  A  lady  bought  9  curtains  at  $5  eachj  she 
gave  the  salesman  5  ten-dollar  bills;  she  should 

receive  in  change  . 

(i)  A  gentleman  bought  4  horses  at  $120  each; 
he  gave  in  payment  5  one-hundred-dollar  bills ;  he 
should  receive  in  change  dollars. 


Copy  and  subtract: 

87i              436 

526 

636 

34.6 

24f              208 

319 

117 

12.8 

PART    II.  133 

1.  Think  of  an  oblong  3  feet  by  10  feet. 
Tliink  of  it  divided  into  1-foot  squares.  The  area 
of  the  oblong  is  square  feet. 

2.  The  perimeter  of  an  oblong  3  feet  by  10 
feet  is  feet. 

3.  Think  of  a  floor  6  ft.  by  7  ft.  Think  of  it 
divided  into  1-foot  squares.  The  area  of  a  floor  6 
ft.  by  7  ft.  is  square  feet. 

4.  The  perimeter  of  a  floor  6  ft.  by  7  ft.  is 
feet. 

5.  The  first  day  of  October,  1895,  was  Tuesday; 

the  second  Tuesday  of  October  was  the  th 

day  of  the   month;    the  third  Tuesday  was  the 

th;    the  fourth  Tuesday  was  the  ;  the 

fifth  Tuesday  was  the  . 


6.  The  Mondays  of  September,  1895,  were  the 
2nd,  ,  ,  ,  and  . 

7.  Harry  rode  45  miles  in  5  hours;  he  rode  at 
the  rate  of  miles  an  hour.     45  ^  5  = 

8.  James  rode  46  miles  in  5  hours;  he  rode  at 
the  rate  of  miles  an  hour.     46  -^  5  = 

9.  Richard  rode  48  miles  in  5  hours;  he  rode 
at  the  rate  of  miles  an  hour.     48  -^  5  = 

10.     At  20^  a  peck,  3  pecks  of  apples  cost 

cents;  8^  pecks  cost  ■. 

Copy  and  multiply : 

63i  521  741  831  92^ 

2  2  2  2  2 


134  ELEMENTARY    ARITHMETIC. 

1.  A  year  that  is  not  a  leap-year  is  sometimes 
called  a  common  year.     In  a  common  year  there 

are  365  days.     365  days  -^  7  days  =  .     In  a 

common  year  there  are  weeks  and day. 

2.  If  the  first  day  of  a  common  year  is  Monday, 
the  first  day  of  the  next  year  will  be . 

3.  We  may  think  of  a  year  as  beginning  at 
any  time  and  ending  on  the  same  day  of  the  same 
month  of  the  next  year;  tlms,  it  is  a  year  from 
April  10,  1894,  to  April  10,  1895;  it  is  a  year 
from  May  4,  1895,  to  May  4,  1896. 

4.  Any  year  in  which  there  is  a  February  29th 
contains  366  days;  all  other  years  contain  . 

5.  From  February  10th  of  a  leap-year  to  Feb- 
ruary 10th  of  the  next  year  it  is  days.     366 

days  -^  7  days  = 

6.  If  February  10th  of  a  common  year  is 
Wednesday,  February  10th  of  the  next  year  will 
be  . 

7.  If  February  10th  of  a  leap-year  is  Wednes- 
day,  February    10th    of    the    next    year    will    be 


8.  From  March  Isfc  of  a  leap-year  to  March  1st 

of  the  next  year  it  is  days.     If  March  1st  of 

a  leap-year  is  Monday,  March  1st  of  the  next  year 
will  be  . 

Copy  and  divide : 

4^)56^  4^)96^  4^)64^  4^)104^ 


TART  II 


135 


1.  One  half  is  

2.  One  fifth  is  

3.  Three  fifths  are 

4.  Two  fifths  are  - 

5.  Four  fifths  are 


tenths, 
tenths. 

tenths. 

—  tenths. 

—  tenths. 


6.  Acid  1  half  and  1  fifth. 

1  half  is  tenths. 

1  fifth  is  tenths. 

—  tenths  and  tenths  are 


7.  Add  2  fifths  and  1  half. 

2  fifths  are  tenths. 

1  half  is  tenths. 

—  tenths  and  tenths  are 


8.  From  4  fifths  subtract  1  half. 

4  fifths  are  tenths. 

1  half  is  tenths. 

—  tenths  less  tenths  are 


tenths. 


tenths. 


tenths. 


9. 


are 


One  fifth  of  a  dollar  and  1  half  of  a  dollar 
—  tenths  of  a  dollar. 


Copy  and  divide : 

4)56^  4)96^ 


4)64^ 


4)104^ 


136  ELEMENTARY    ARITHMETIC. 


E 


I    I    I    I       I    I    I    I    I  I    I    I    I   r 


'T 


1 .  -^  of  an  inch  +  I-  of  an  inch  =        ^  -|-  -^  _ 

2 .  4^  of  an  inch  —  ^  of  an  inch  =        ^  —  -i-  = 

3.  I  of  an  inch  x  2  =  -^  X  2  = 

4.  ^  of  an  inch  x  2^  =  i-  X  2|  = 

5.  5  inches  ^  4^  of  an  inch  =  5  -^  -|^  = 

6.  4-  of  ai^  inch  ^  5  —  ^  -^  5  = 

7.  Draw  a  line  3^  inches  long;  erase  from  it 
inches;  the  line  that  is  left  is  and  

inches  long.     S^  —  2^  = 


8.  Draw  a  line  34  inches  long;   erase  from  it 

1|  inches;  the  line  that  is  left  is  and  

inches  long.     3^  —  1-5  = 

9.  Harry  drew  an  oblong;    it  was  1^  inches 

wide  and  l^^  inches  long;  its  perimeter  was  

and inches. 

10.  Arthur  had  a  piece  of  silver  wire;  it  was 
14  inches  long;  he  wished  to  divide  into  pieces  4- 

of  an  inch  long;  he  could  make  such  pieces 

and  have of  an  inch  left. 

11.  James  had  a  piece  of  copper  wire;  it  was 
1.5  inches  long;  he  divided  it  into  three  equal 
pieces;  each  piece  was 


Copy 

and  add: 

24^ 

324 

32 

163 

m 

245 

long. 

136 

252 

20.5 

252 

347 

34.2 

344 

142 

61.6 

PART  II.  137 

12  nines  are  108  11  nines  are  99 

9  twelves  are  108  9  elevens  are  99 

1.  Can  you  add  column  (a)  in  fifteen  seconds, 
beginning  at  the  top? 


2.  Can  you  add  column  (a) 
in  fifteen  seconds,  beginning  at 

a 

9 
9 

b 

2 
9 

c 
4 
9 

d 

6 
9 

e 
9 
6 

the  bottom? 

9 

9 

9 

9 

9 

3.  Practice  until 

I  you  can  do 

9 
9 

9 
9 

9 
9 

9 
9 

9 

this  with  each  column. 

9 

9 

9 

9 

8 

4.  Ten  nines  are 

» 

9 
9 

9 
9 

9 
9 

9 
9 

9 
1 

5.  Eleven  nines 

are  . 

9 

9 

9 

9 

9 

6.  Twelve  nines 

are  . 

9 

9 

9 

9 

2 

7.  Twenty  nines 

!  are  . 

9 
9 

9 
9 

9 
9 

9 
9 

9 

8.  27  +  9  = 

17  +  9  = 

1 

3 

5 

7 

9 

9.  37  +  9  = 

57  +  9  = 

4 
9 

10.  46  +  9  = 

16  +  9  = 

85  +  9 

— 

5 

11.  26  +  9  =. 

56  +  9  = 

73 

+  9 

= 

9 

6 

12.  38  +  9  =. 

18  +  9  = 

47 

+  9 

9 

13.  48  +  9  = 

28  +  9  = 

64  +  9 

= 

14.  25  +  9  - 

15  +  9  = 

35  +  9 

= 

15.  65  +  9  = 

45  +  9  = 

75 

+  9 

= 

Copy  and  subtract: 

754-               370 

640 

750 

84 

321               128 

239 

34' 

7 

31.6 

138  ELEMENTARY    ARITHMETIC . 

1.  7  is  contained  in  15 times  and over. 

2.  7  is  contained  in  15 and times. 

3.  7  is  contained  in  16 times  and over. 

4.  7  is  contained  in  16  — —  and times. 

5.  7  is  contained  in  18 times  and over= 

6.  7  is  contained  in  18 and times. 

7.  7  is  contained  in  23 times  and over. 

8.  7  is  contained  in  23 and times. 

9.  7  is  contained  in  30 times  and over. 

10.  7  is  contained  in  30 and — -  times. 

11.  7  is  contained  in  38 and times. 

.   12.  7  is  contained  in  43 and times. 

13.  7  is  contained  in  45 and times. 

14.  7  is  contained  in  40 and times. 

15.  7  is  contained  in  50 and times. 

16.  Wiien  milk  is  7^  a  quart,  for  18^  I  can  buy 
and quarts.     18^  -^  7^  = 

Read  first  by  column,  then  by  line. 

4  2's  are .     4  5's  are .     4  8's  are . 

4  3's  are .     4  6's  are .     4  9's  are ■. 

4  4's  are .     4  7's  are .     4  lO's  are . 


Copy  and  multiply : 

43i  54i  72h  61i  92^ 

3  3  3  3  3 


PART  II.  139 

1.  If  a  man's  wages  are  $40  for  5  weeks,  in 
one  week  he  earns  dollars. 

(a)  If  a  man's  wages  are  $215  for  5  months, 
how  much  does  he  earn  in  one  month? 

2.  If  6  barrels  of  flour  are  worth  $30,  2  barrels 
are  worth  dollars. 

(b)  If   6   acres  of  land  are  Avorth   $264,  how 
much  are  2  acres  worth? 

3.  At  4^  each,  for  32^  I  can  buy pencils. 

(c)  At  4^  each,  how  many  pencils  can  be  bought 

for  $8.24? 


4.  Forty-eight  quarts  are  gallons. 

(d)  How  many  gallons  are  572  quarts? 

5.  Eighty  pints  are  gallons. 

(e)  How  many  gallons  are  440  pints? 

6.  A  grocer  sold  2  barrels  of  apples  at  $2.30 
each;  he  received  for  them  . 

(f )  A  farmer  sold  8  barrels  of  apples  at  $2.30 
each.     How  much  should  he  receive  for  them? 

Read  first  by  column,  then  by  line. 

5  2's  are .       5  5's  are  — -.        5     8's  are . 

5  3's  are .       5  6's  are .        5     9's  are . 

5  4's  are -.       5  7's  are .       5  lO's  are . 


Copy  and  divide: 

5^)65^  5^)115^  5^)75^  5^)125^ 

—  times 


140  ELEMENTARY    ARITHMETIC. 

1.  January  1st,  1897,  was  Friday.  January 
1st,  1898,  was .    January  1st,  1899,  was . 

2.  July  4th,   1897,  was   Sunday.      July  4tli, 

1898,  was  .     July  4tli,  1899,  was  . 

3.  December  25tli,  1897,  was  Saturday.  De- 
cember 25tli,  1898,  was  .     December  25th, 

1899,  was  . 

4.  A  man  paid  6  hundred  dollars  for  a  piece 
of  land;  he  spent  1  hundred  dollars  in  improving 
it,  and  sold  it  for  9  hundred  dollars;  he  gained 
— ■■ —  hundred  dollars. 

(a)  A  man  paid  614  dollars  for  a  piece  of  land; 
he  spent  136  dollars  in  improving  it,  and  sold  it 
for  975  dollars;  he  gained . 

5 .  A  man  paid  5  hundred  dollars  for  a  house ; 
he  paid  1  hundred  dollars  for  repairing  it;  he  sold 

the  house  for  8  hundred  dollars;  he  gained  

hundred  dollars. 

6.  Mary  bought  5^  worth  of  pens,  10^  worth 
of  paper,  and  3^  worth  of  gum;  if  she  gave  the 
salesman  a  quarter  of  a  dollar,  how  much  change 
should  she  receive? 

7.  Peter  rode  36  miles  in  4  hours;  he  rode  at 
the  rate  of  miles  per  hour.     36  -^  4  = 

8.  Paul  rode  37  miles  in  4  hours;  he  rode  at 
the  rate  of  miles  per  hour.     37  ^  4  = 

Copy  and  divide: 

5)65(^  5)115^  5)75^  5)125^ 


PART  II 


141 


6  eights  are  48         6  nines  are  54 
8  sixes  are  48  9  sixes  are  54 

7  eights  are  56         8  sevens  are  56 

7  sevens  are  49 


1.  Forty-eight  quarts  are 

2.  Forty-nine  days  are  — 


3.  Fifty-four  spoons  are 

4.  Fifty-six  days  are  — 

5.  7  pecks  are  — 

6.  8  Aveeks  are  — 


—  pecks, 
weeks. 

-  sets. 


weeks. 


7.  Fifty  inches  are 

8.  Fifty  days  are  - 

9.  Fifty  quarts  are 


10.  Seven  weeks  and  3  days  are 

11.  Four  feet  and  5  inches  are  - 


quarts.     6  pecks  = 
days.     7  weeks  = 

—  feet  and inches. 

—  weeks  and  day. 

—  pecks  and quarts. 


days. 


—  inches. 
12.  Twelve  bushels  and  3  pecks  are pecks. 


13.  2f  are 

14.  4|  are 


sevenths.  3^  are 
sevenths.  5f  are 


sevenths, 
sevenths. 


Read  first  by  column,  then  by  line. 

6  2's  are .     6  5's  are .     6  8's  are 

6  3's  are .     6  6's  are .     6  9's  are 

6  4's  are .     6  7's  are .     6  lO's  are 


Copy  and  add: 

33-1-      526 

628 

731 

83.6 

25      234 

204 

229 

21.4 

41|-      312 

325 

402 

23.5 

142  ELEMENTARY    ARITHMETIC. 

1.  Add  5  gal.  2  qt.  and  5  gal.  3  qt. 

(a)  Add  124  gal.  2  qt.  and  31  gal.  3  qt. 

2.  From  tlie  sum  of  9  and  5,  subtract  10. 

(b)  From  the  sum  of  236  and  72,  subtract  104. 

3.  Multiply  6  by  3  and  to  the  product  add  6. 

(c)  Multiply  125  by  3  and  to  the  product  add 
125. 

4.  Divide  12  by  2  and  multiply  the  quotient 

by3.        _ 

(d)  Divide  256  by  2  and  multiply  the  quotient 
by  3. 

5.  Two  thirds  of  18  inches  are  inches. 

(e)  Two  thirds  of  126  inches  are inches. 

6.  Eighteen  inches  are  f  of  inches. 

(f )  One  hundred  and  twenty-six  inches  are  f  of 
inches. 

7.  A  man  paid  8  hundred  dollars  for  a  house; 
he  repaired  it  at  a  cost  of  4  hundred  dollars,  and 
sold  it  for  10  hundred  dollars;  he  lost  hun- 
dred dollars. 

(g)  A  man  paid   836   dollars  for  a  house;  he 
repaired  it  at  a  cost  of  124  dollars  and  sold  it  for 


Copy 

lXcXIDj      lie    J.UC5U 

and  subtract: 

671 

408 

509 

706 

80.4 

34| 

240 

360 

450 

55 

PART  II. 


143 


1.  Observe  the  diagram  given  below.  It  is  an 
oblong  2  inches  by  3^  inches.  Think  of  it  as  made 
up  of  two  rows  of  1-inch  squares  with  a  piece  of 
another  square  at  one  end  of  each  row.     The  piece 

is of  a  square  inch.    In  each  row  there 

are  and square  inches.      3|  sq. 

in.  X  2  =  .     The  area  of  an  oblong  2  inches 

by  3^  inches  is  . 


M  ill 

T— t 

liu. 

lin. 

1  in. 

d 

•  r-l 

2.  Draw  an  oblong  4^  inches  by  2  inches. 
Divide  it  as  far  as  possible  into  1-inch  squares. 
It  contains  two  rows  of  figures.    In  each  row  there 

are  and square  inches.    The  area 

of  an  oblong  4^  inches  by  2  inches  is  . 


Copy  and  multiply: 

31i  41^ 

4  4 


5U 


611 
4 


71i 
4 


144  ELEMENTARY    ARITHMETIC. 

1.  February  1st,  1897,  was  Monday.    February 
1st,  1898,  was  .     February   1st,   1899,  was 


2.  April  1st,  1897,  was  Thursday.     April  1st, 
1898,  was  .     April  1st,  1899,  was  -. 

3.  May  1st,  1897,  was  Saturday.     June   1st, 
1897,  was  . 

4.  Two  thirds  of  12  are  one  half  of  . 

5.  One  half  of  16  is  two  thirds  of  . 


6.  Two  thirds  of  15  are  one  half  of 

7.  One  half  of  20  is  two  thirds  of  - 


8.  Peter  rode  56  miles  in  7  hours;  he  rode  at 
the  rate  of  miles  an  hour. 

9.  Harris  rode  57  miles  in  7  hours;  he  rode  at 
the  rate  of  miles  an  hour. 

10.  Adam  rode  59  miles  in  7  hours;  he  rode  at 
the  rate  of  miles  an  hour. 


11.  22  thirds  are .     22  fourths  are 

12.  22  fifths  are  .      22  sixths  are  - 

13.  24  fifths  are  .      25  sixths  are  - 


14.  I  am  thinking  of  a  triangle,  each  side  of. 
which  is  9  inches.     The  perimeter  of  this  triangle 
is  inches. 

Copy  and  divide: 

|6)$126    $6)$186    $6)$192    $6)$204 


PART  II. 


145 


1.  One  fourth  is 

2.  One  sixth  is  - 


twelfths. 


—  twelfths. 
3.  Three  fourths  are  twelfths. 


4.  Five  sixths  are 


twelfths. 


5.  Add  1  fourth  and  1  sixth. 

1  fourth  is  twelfths. 

1  sixth  is  twelfths. 

—  twelfths  and twelfths  are 


twelfths. 


6.  Add  3  fourths  and  1  sixth. 

3  fourths  are  twelfths. 

1  sixth  is  twelfths. 

—  twelfths  and twelfths  are  — 


twelfths. 


7.  From  5  sixths  subtract  1  fourth. 

5  sixths  are  twelfths. 

1  fourth  is  twelfths. 

—  twelfths  less twelfths  are  — 


—  twelfths. 

8.  One  sixth  of  a  foot  and  1  fourth  of  a  foot 
are  twelfths  of  a  foot. 

9.  Three  fourths  of  a  foot  less  1  sixth  of  a  foot 
are  twelfths  of  a  foot. 


Copy  and  divide : 

6)$126     6)$186 


6)$192     6)$204 


146 


ELEMENTARY    ARITHMETIC. 


1. 

2. 
3. 
4. 
5. 
6. 


I-  of  a  foot  +  ^  of  a  foot  = 
I-  of  a  foot  —  |-  of  a  foot  = 
4  of  a  foot  X  3  = 


4-  of  a  foot  X 


^  1 
o4  = 


2  feet  ^  I  of  a  foot 


of  a  foot 


1  -I-  1 


1 
T 


|x3  = 

TT    X     O-o- 


1 

T 


7.  Draw  a  line  4^  feet  long; 
feet  long;  together  the  Imes  are 
feet  long.     4|  +  2|  = 


draw  another  2- 
—  and  


41  —  21 


8.  Draw  a  Ime  4|-  feet  long;  erase  from  it  2|^ 

feet;  the  line  that  is  left  is  and 

feet  long.     4|- -  2|  =  4|- +  2|  == 

9.  The  perimeter  of  a  l-|^-foot  square  is  

feet.     U  +  U  +  U+U=  U  x  4  =. 


10.  Richard  had  a  piece  of  silver  wire  2|-  feet 
long ;  he  wished  to  divide  it  into  pieces  -g-  of  a  foot 

—  such  pieces  and  have 


long;  he  could  make  — 
of  a  foot  left. 


11.  Ned  had  a  piece  of  rope  11^  feet  long;  he 

divided  it  into  2  equal  parts ;  each  part  was  

and feet  long.     lli-^2=      ^  of  lU - 


12.  12  ft. 

13.  14  ft. 

14.  12  ft. 


2=     13  ft.  -  2 


15  ft. 


1  '^ 


hit. 


2 

2  = 


2  =     151  ft.  -  2  == 


13  ft.  -  3  =     131  ft. 


Copy  and  add: 

482 

31  214 

22|  224 


24| 


346 

252 
172 


425 
370 
125 


34.3 
25.3 
12.4 


PART  II. 


147 


REVIEW. 


1. 

2. 
3. 
4. 
5. 

6. 
7. 
8. 

9. 
10. 
11. 
12. 


'  + 


"2" 


+ 


1       _ 

T  — 

jL  _ 

6    ~ 
i    

1  _ 

To"  ~ 

1  _ 

T^  - 


+  i  = 


1 
T 

1  I     1    _ 

T  '    T  — 

1  I       1     _ 

■S"  I     TY  - 

111    — 

T  ^  ¥  — 

1  I       1     _ 

T  r  i-g-  - 


"5"  +  T^ 


1     _ 


+ 


1     _ 


1 

1 
2 
1 

a 

1 

1 

3 


1 
3 
1, 
3 
1 

1 

T 

1 

T 

1 

5 

1 


1    _ 
T  — 

X  — 
6    ~~ 

1    — 

8  ~ 

1      _ 

TTT  - 

1      _ 

TW  ~ 

1    _ 

T  ~ 

X  — 

9  ~ 

1      _ 

1  2   - 

1  _ 

8    ~ 

1      _ 

1      _ 
TTT  - 

1     _ 

y^  - 


1 

1 
2 
1 
2 
1 

"2" 
1 
2 


1 

T 
1 
T 

5 
1 


X  4::= 

X  5    = 

X  3  = 

X  G  = 

X  7- 


4x6 
4  x 


4:    = 


i  X  o 


X  8  = 

X  5  = 

X  10:. 

X  18::: 


13.  Can  you  read  the  first  12  lines  on  this  page, 
completing  each  statement  correctly,  in  2  minutes? 
Try  to  do  this. 

14.  I  can  change  halves  to  4ths,  to  — ,  to 

,  to  ,  to  . 

15.  One  half  is   twentieths. 

fortieths. 

16.  One  half  is  — 
dredths. 


1 

"2" 


IS 


fiftieths.     4-  is 


hun- 


Copy  and  subtract: 

37      518      416 

25|      240      150 


617 
460 


71.8 
36. 


148 


ELEMENTARY    ARITHMETIC. 


1.    6- 

1 

2 

2.  5 

1 

3.  4- 

1 

4.  4 

1 

3 

5.  3 

3 


4,  means 
6,  means 

■I,  means 

5,  means 

^,  means 
4  J  means 

I,  means 
4,  means 

I,  means 
3,  means 


-^  IS  con 


-^  IS  con 
iof  — 


6.  One  half  of -j^  is 

7.  One  half  of  ^  is 


-.    loi 


2   ^-^  Y'ff  1^ 

h  of  yV  is 


8.  4-  is  contained  in  2 

9.  |-  is  contained  in  2 

10.  ^  is  contained  in  2 

11.  -i^  is  contained  in  2 

12.  ^  is  contained  in  3 


times, 
times, 
times, 
times, 
times. 


1 

T 

X 
5 

J_ 
6 

J_ 
9 

1  0 


13. 
14. 
15. 
16. 


2| 


1 

3 

1 

T 

1 
5 

6 


-  ^ 

2| 


1  _ 

3  ~ 

1  _ 

T  — 

J_  _ 

5  ~ 

X  — 

6  ~ 


34  -^ 


Ri 

«->-/(- 


*>  1 


^1 


3| 

^  3 


Or 


Q5 


Copy  and  multiply : 


324 


22-^- 


424- 


42|- 


421 
5 


PART  II.  149 

REVIEW. 

12_|_1_  2_1_  2    ^    A    — 

2.|  +  i=  i-i=  |x5  = 

3.|  +  A=  |-A=  Ix6  = 

4.34_1_  3_1_  3v/2   — 

K3il_  3_1_  3v^   — 

C       2      \        1      —  2_1_  2w4._ 

721        3      _  2_3_  2    Ky    a   — 

'•"51     TO"—  5"  TIJ—  5-^^   — 

8.  1  +  I  =  (Change  to  6tlis.)  i  +  I  = 

9.  4-  -  I  =  (Change  to  .)  |  -  |  = 

10.  I  +  ^  =  (Change  to  .)  |  +  i  - 

11.  I  -  I  =  (Change  to  .)  |  -  i  = 


TESTS. 


If  pupils  have  mastered  the  work  up  to  this  point,  they 
will  have  no  difficulty  with  the  following.  The  real  test  is 
the  pupil's  power  to  do  that  which  he  has  not  done  before. 

(a)  Can  you  add  ^  and  i?     (Change  to  .) 

(b)  Can  you  subtract  ^  from  |  ?  (Change  to .) 

(c)  Can  you  add  f  and  ^2     (Change  to  .) 

(d)  Can  you  add  i  and  -^2     ^  and  -^-^2 

(e)  Multiply  I  by^7.       |  by  12.     |  by  6^. 

(f)  Multiply  8 1  by  6.     |  by  60.     4  by  7|. 

(g)  Multiply  6|  by  8.     |  by  20.     |  by  40. 

Copy  and  divide : 

$3)$127    $3)$154    $3)$217    S3)$184 


150  ELEMENTARY   ARITHMETIC. 

1.  Divide  2  thirds  by  1  fourth. 

2  thirds  are  twelfths. 

1  fourth  is  twelfths. 

12ths  in  12ths  and  times. 


2.  Divide  3  fourths  by  1  third. 

3  fourths  are  12ths. 

1  third  is  twelfths. 

12ths  in  12ths  and  - —  times. 

3.  Divide  1  half  by  1  fifth. 

1  half  is  tenths. 

1  fifth  is  tenths. 

tenths  in  tenths  and —  times. 

4.  Divide  ^  by  ^3.  (Change  to  sixths.) 

5.  Divide  -f-  by  \.  (Change  to  eighths.) 

6.  Divide  -|  by  -f-  (Change  to  ninths.) 

7.  Divide  -|-  by  -^.  (Change  to  tenths.) 

8.  -I  -^-  YQ-  =         Yjj  oi  £1  dollar  is  contained  in 
f  of  a  dollar  times. 

9-  T  "^  TT  —  tV  of  ^  foot  is  contained  in  | 

of  a  foot  times. 

10.  i  ^  -J-  =         |-  of  a  pie  is  contained  in  1^  of 
a  pie  times. 

11.  |.  ^  |-  =         ^  of  a  foot  are  contained  in 
3^  of  a  foot  and times. 

Copy  and  divide : 

4)$129     4)^169     4)$2Q9     4)$210 


PART  II.  151 


7  nines  are  63         9  eights  are  72 
9  sevens  are  63       8  nines  are  72 

8  eights  are  64       9  nines  are  81 


'■&■' 


1.  Sixty-three  days  are  weeks. 

2.  Sixty-four  quarts  are  pecks. 

3.  Seventy-two  pints  are  gallons. 

4.  Eighty-one  ninths  are  Avholes. 

5.  Ninety  inches  are feet  and inches. 

6.  Ninety  days  are weeks  and days. 

7.  Nine  weeks  and  2  days  are  days. 

8.  Seven  feet  and  5  inches  are  inches. 

Read  first  by  column,  then  by  line. 

7  2's  are .     7  5's  are .     7  8's  are 

7  3's  are .     7  6's  are .     7  9's  are 

7  4's  aj^e .     7  7's  are .     7  lO's  are 


8  2's  are .     8  5's  are .  8  8's  are 

8  3's  are .     8  6's  are .  8  9's  are 

8  4's  are .     8  7's  are .  8  lO's  are 

9  5's  are .  9  8's  are 

9  6's  are .  9  9's  are 

9  7's  are .  9  lO's  are 


9  2's 

are  - 



9  3's 

are  - 

. 

9  4's 
Cop 

y  and  add: 

26| 

432 

12 

200 

20i 

148 

546  342  36.2 

84  108  31.3 

225  705  32.6 


152 


ELEMENTARY    ARITHMETIC. 


2  times  2 

3  times  2 

4  times  2 

5  times  2 

6  times  2 

7  times  2 

8  times  2 

9  times  2 

2  times  5 

3  times  5 

4  times  5 

5  times  5 

6  times  5 

7  times  5 

8  times  5 

9  times  5 

2  times  8 

3  times  8 

4  times  8 

5  times  8 

6  times  8 

7  times  8 

8  times  8 

9  times  8 


are  4. 
are  6. 
are  8. 
are  10. 
are  12. 
are  14. 
are  16. 
are  18. 

are  10. 
are  15. 
are  20. 
are  25. 
are  30. 
are  35. 
are  40. 
are  45. 

are  16. 
are  24. 
are  32. 
are  40. 
are  48. 
are  56. 
are  64. 
are  72. 


TABLES. 

2  times  3  are  6. 

3  times  3  are  9. 

4  times  3  are  12. 

5  times  3  are  15. 

6  times  3  are  18. 

7  times  3  are  21. 

8  times  3  are  24. 

9  times  3  are  27. 


2  times  6 

3  times  6 

4  times  6 

5  times  6 

6  times  6 

7  times  6 

8  times  6 

9  times  6 

2  times  9 

3  times  9 

4  times  9 

5  times  9 

6  times  9 

7  times  9 

8  times  9 

9  times  9 


are  12. 
are  18. 
are  24. 
are  30. 
are  36. 
are  42. 
are  48. 
are  54. 

are  18. 
are  27. 
are  36. 
are  45. 
are  54. 
are  63. 
are  72. 
are  81. 


2  times  4 

3  times  4 

4  times  4 

5  times  4 

6  times  4 

7  times  4 

8  times  4 

9  times  4 


are  8. 
are  12. 
are  16. 
are  20. 
are  24. 
are  28. 
are  32. 
are  36. 


2  times 

3  times 

4  times 

5  times 

6  times 

7  times 

8  times 

9  times 

9  and  4 

8  and  5 

7  and  6 

9  and  5 
9  and  6 

8  and  7 

9  and  7 
9  and  8 


7  are  14. 
7  are  21. 
7  are  28. 
7  are  35. 
7  are  42. 
7  are  49. 
7  are  56. 
7  are  63. 

are  13. 
are  13. 
are  13. 
are  14. 
are  15. 
are  15. 
are  16. 
are  1  7. 


PART    III. 


DECIMALS TENTHS. 


1.  6^  and  2^  are  cents. 

2.  .6  and  .2  are  tenths. 

3.  6^  less  2^  are  cents. 

4.  .6  less  .2  are  tenths. 

5.  4^  X  2,  means,  ^  times  Jf(^;  2  times  4^  are 


6.  .4x2,  means,  2  times  .Jf;    2  times  .4  are 


7.  6^  -^  2^,  means,  y^nt^  Aoi';  ma?i?/  /zmes  2(^  are 
contained  in  6^;  2^  are  contained  in  6^ times. 

8.  .6  -h  .2,  means,  find  Jioiv  many  times  .2  are 
contained  in  .6 ;  .2  are  contained  in  .6  times. 

9.  6^  -^  2,  means, ^?icZ  one  half  of  .6^;  one  half 
of  6^  is  cents. 

10.  .6^2,  means,  find  one  half  of  .6 ;  one  half 
of  .G  is ■  tenths. 

Copy  and  multiply : 

244-  23.6  24.8  34.9  231 

4  2  2  2  G 


153 


154  ELEMENTARY    ARITHMETIC. 

DECIMALS TENTHS. 

1.  One  tenth  of  a  dollar  =  dime.     $.2 

2.  One  tenth  of  a  dollar  =  cents.      $.3 

3.  Three  tenths  of  a  dollar  = dhnes.  $.5 

4.  Four  tenths  of  a  dollar  =  cents.   $.6 

5.  Fifty  cents  =  dimes.     Seventy  cents 

6.  Sixty  cents  =  tenths  of  a  dollar. 

7.  Eight  dimes  =  tenths  of  a  dollar. 

8.  $.8  = dimes.     $.8  = cents. 

9.  %.d  =  cents.     $.9  =  dimes. 

10.  $1.2  = dollar  and dimes.    $1.4 

11.  $1.2  := dimes.     $1.4  = dimes. 

12.  $1.2  == dollar  and cents.     $1.5 


13.  Mary  had  $.4  in  her  pocket  and  $.3  in  her 
bank  ;  in  both  she  had  . 

14.  Jane    had    $.9;    she    spent    $.3;   she   then 
had  . 

15.  Sarah  jwd  $.4  for  each  of  three  books;  for 
all  she  paid  . 

16.  Alice  had  $.8  with  which  to  buy  tea  at  $.4 
a  pound  ;  she  'could  buy  pounds. 

17.  Maude  paid  $.6  for  two  pounds  of  coffee; 
one  pound  cost . 

Copy  and  divide : 

$.3)$24.6^  $.4)$25.2  $.5)$27.5 
times 

*Observe  that  the  puijil  is  required  to  find  how  many  times 
3  tenths  are  contained  in  216  tenths — 3  dimes  in  246  dimes. 


PART  III.  155 

DECIMALS TENTHS. 

1 ,    .5  +  'S.      (To  be  read,  5  tenths  plus  3  tenths.) 

.5  --h  .3,  means,  .5  and  .3.     .5  and  .3  are  

tenths.     Arthur  earned  .5  of  a  dollar  Monday  and 
.3  of  a  dollar  Tuesday;   in  both  days  he  earned 


2.  .9  —  .4.       (To  be  read,  .9  tenths  minus  4  tenths.) 

.9  —  .4,  means,  .9  less  .4.     .9  less  .4  are  

tenths.     Harry  had  .9  of  a  dollar;  he  spent  .4  of 
a  dollar;  he  then  had  . 

3.  .4x3.      (To  be  read,  4  tenths  multiplied  by  3.) 
.4x3,  means,  S  times  .Jf,     3  times  .4  are 


tenths.     If  one  yard  of  ribbon  is  worth  .4  of  a 

dollar,  3   yards  are  worth  tenths,  or 

and  tenths  dollars. 

4.  1.2  -^  .4.  (To  be  read,  12  tenths  divided  by  4  tenths.) 
1.2  ^  .4,  means,  find  how  many  times  .Jf  are  con- 
tained in  1.2,      A  are  contained  in  1.2  . 

James  had  1.2  dollars  with  which  to  buy  tea  at  .4 
of  a  dollar  a  pound ;  he  could  buy  pounds. 

5.  1.2  -^  4.      (To  be  read,  12  tenths  divided  by  4.) 

1.2  H- 4,  means,  find   one  fourth  of  1.2.     One 

fourth  of  1.2  is  tenths.      William  jDaid  1.2 

dollars  for  4   pounds  of  coffee;    one  pound  cost 
tenths  of  a  dollar. 

Copy  and  divide : 

3)$24.6  4)$25.2  5)$27.5 


156  ELEMENTARY   ARITHMETIC. 

DECIMALS TEXTHS. 

1.  The  sum  of  5.2  and  4.3  ls .  3.5  +  3.5  = 

2.  The  sum  of  4.6  and  4.6  is .  5.Q  +  5.6  = 

3.  The  sum  of  3.6  and  4.6  is .  3.7  +  3.7  = 

4.  The  sum  of  4.7  and  5.7  is .  4.8  +  5.8  ^ 

5.  10.2  +  10.2=  10.8  +  10.8  = 

6.  10.2  +  12.2  =  20.3  +  20.3  = 

7.  20.9  +  20.9  =  20.6  +  20.7  = 

8.  23.4  +  20.4  =  23.5  +  22.4  = 

9.  23.6  +  22.6  =  23.7  +  32.7  = 

10.  The  sum  of  two  and  six  tenths,  and  four 
and  three  tenths  is  — . 

11.  Tlie  sum  of  eight  and  three  tenths,  and  four 
and  two  tenths  is  . 

12.  Joseph  paid  $6.5  for  a  suit  of  clothes  and 
$2.2  for  a  hat;  for  both  he  paid  — . 

13.  In  the  month  of  September  the  rainfall  in 
Chicago  was  3.4  inches;  in  October  it  was  2.6 
inches;  in  both  months  it  was  . 

(a)  Find  the  sum  of  25.3,  34,  and  24.2. 

(b)  Find  the  sum  of  31.3,  25,  and  32.2. 

(c)  Find  the  sum  of  26.4,  35,  and  12.6". 

(d)  Find  the  sum  of  25.5,  37,  and  23.4. 

(e)  Find  the  sum  of  31.2,  44,  and  20.5. 

(f )  Find  the  sum  of  42.5,  36,  and  22.2. 

(g)  Find  the  sum  of  35.3,  28,  and  32.4. 
(h)  Find  the  sum  of  34.2,  34,  and  34.3. 


PART  III.  157 

DECIMALS TENTHS. 

1.  The  difference  of  8.6  and  4.3  is  . 

2.  The  difference  of  8.2  and  .6  is  . 

3.  The  difference  of  8  and  4.2  is  . 

4.  The  difference  of  8.5  and  1.6  is  . 

5.  20.6  -  10.2  =  20.6  +  10.2  = 

6.  15.5  -  10.3  =  15.5  +  10.3  = 

7.  20.2  -  10.6  =  20.2  +  10.6  = 

8.  23.8  -  10.5=  23.8  +  10.5  = 

9.  Cyrus  had  $4.6;  he  paid  $2.5  for  a  book; 
he  then  had  . 


6  = dollars  and  cents. 

$2.5  =  dollars  and  cents. 

$2.1  =  - — -  dollars  and  cents. 

10.  A  farmer  received  $4.7  for  a  sheep  and  $3.5 

for  a  pig;    for  both  he   received  and  — — 

tenths  dollars. 

$4.7  =  dollars  and  cents. 

$3.5  =  dollars  and  cents. 

.2  =  dollars  and  cents. 


(a)  From  forty -three  and  eight  tenths  dollars 
take  one  and  four  tenths  dollars. 

(b)  From  twenty-five  and  three  tenths  dollars 
take  twelve  and  two  tenths  dollars. 

(c)  From  75.3  subtract  28.1. 

(d)  From  36.2  subtract  12.4. 

(e)  From  84.7  subtract  2.9. 


158  ELEMENTARY    ARITHMETIC. 


DECIMALS TENTHS. 

1.  The  product  of  8.3  and  2  is 

2.  The  product  of  3.5  and  2  is 

3.  The  product  of  2.4  and  3  is 

4.  The  product  of  1.5  and  4  is 


5.  3.2  X  3=  3.2  +  3=  3.2-3  = 

6.  2.1  X  4  =  2.1  f  .4  =  2.1  -  A  = 

7.  2.3  X  4=  2.3  +  4=  2.3-  .4  = 

8.  2.5  X  5=  2.5 +  .5=  2.5  -  .5  = 

9.  At  $4.5  a  cord,  3  cords  of  wood  will  cost 

.     $6.5x3  = 


10.  A  man  had  $5.3  in  one  pocket  and  $3.9  in 
another ;  in  both  he  had  . 

11.  Chester  had  $6.3;  Elmer  had  $5.1;  Chester 
had  dollars  more  than  Elmer. 

12.  15    tenth-dollars  =  and tenths 

dollars. 

13.  2  and  5  tenths  dollars  =  tenth-dollars. 

14.  35    tenth-dollars  =  and  tenths 

dollars. 

15.  1  and  8  tenths  dollars  =  tenth-dollars. 

(a)  Multiply  twenty-four  and  5  tenths  dollars 
by  5. 

(b)  Multiply  thirty-six  and  4  tenths  dollars  by  3. 

(c)  Multiply  forty-two  and  3  tenths  dollars  by  4. 

(d)  Find  the  product  of  37.4  and  2. 

(e)  Find  the  product  of  25.3  and  3. 


PART   III.  159 


DECIMALS TEISTTHS. 


1.  The  quotient  of  $4.5  divided  by  $.5  is 

2.  The  quotient  of  $4.5  divided  by  5  is  — 

3.  The  quotient  of  $3.2  divided  by  $.8  is 

4.  The  quotient  of  $3.2  divided  by  8  is  — 

5.  The  quotient  of  $4.8  divided  by  $.6  is 

6.  The  quotient  of  $4.8  divided  by  6  is  — 

7.  The  quotient  of  $3.0  divided  by  $.5  is 

8.  The  quotient  of  $3.0  divided  by  5  is  - 


9.  The  sum  of  two  numbers  is  15;  one  of  the 
numbers  is  10 ;  the  other  number  is  . 

10.  The  sum  of  two  numbers  is  7.5;  one  of  the 
numbers  is  3.2;  the  other  number  is  . 

11.  The  difference  of  two  numbers  is  4;    the 
greater  number  is  12 ;  the  less  number  is  . 

12.  The  difference  of  two  numbers  is  3.4;    the 
greater  number  is  12.8;  the  less  number  is . 

13.  The  difference  of  two  numbers  is  5;  the  less 
number  is  8 ;  the  greater  number  is  . 

14.  The  difference  of  two  numbers  is  5.3;  the 
less  number  is  8.3;  the  greater  number  is  . 

(a)  Divide  sixty-four  and  two  tenths  by  two 
tenths. 

(b)  Divide  48  and  three  tenths  by  three  tenths, 

(c)  Divide  36  and  eight  tenths  by  four  tenths. 

(d)  Divide  73  and  five  tenths  by  five  tenths. 


160 


ELEMENTARY   ARITHMETIC. 


DECIMALS TENTHS. 


Eead  the  first  ten  lines  twice;  the  first  time  read  1.2, 
twelve  tenths ;  the  second  time  read  it,  one  and  two  tenths,  etc 


1.  One  half  of  1.2  is 

2.  One  third  of  1.2  is  — 

3.  Two  thirds  of  1.2  are 

4.  One  fourth  of  1.2  is  - 


5.  Three  fourths  of  1.2  are 

6.  .8  is  what  part  of  1.2? 

7.  .9  is  what  part  of  1.2? 

8.  .3  is  what  part  of  1.2? 

9.  1.2  is  what  part  of  1.6? 
10.  1.2  is  what  part  of  3.6? 


1.2 
1.2 
1.2 
1.2 
1.2 


=  iof 


—  ¥ 


1 

2 

i^of 


f  of 
iof 
iof 


A  of  1.2? 

.6  of  1.2? 
1.2  of  2.4? 
1.2  of  1.8? 
1.2  of  4.8? 


11.  One  fourth  of  2  (2.0)  is 

1 2 .  Three  fourths  of  2  are  — 

13.  One  fifth  of  2  (2.0)  is  - 

14.  Three  fifths  of  2  are  — 

15.  .4  is of  2.      .5  is 

16.  .8  is of  2. 


—  tenths. 

and tenths. 


—  tenths. 

and tenths. 

of  2. 

Lois of  2. 


(a)  Divide  forty-six  and  four  tenths  by  2. 

(b)  Divide  fifty-two  and  six  tenths  by  2. 

(c)  Divide  forty-five  and  four  tenths  by  2. 

(d)  Divide  sixty-three  and  nine  tenths  by  3. 

(e)  Divide  seventy-two  and  six  tenths  by  3. 

(f)  Divide  eighty-four  and  four  tenths  by  4. 

(g)  Divide  ninety-six  and  fiYQ  tenths  by  5. 


PART  III. 


161 


DECIMALS TEXTHS. 

1.  One  tenth  of  20  is  . 

2.  One  tenth  of  30  is  . 

3.  One  tenth  of  40  is  . 

4.  One  tenth  of  50  is  

5.  Three  tenths  of  20  are  

6.  Three  tenths  of  30  are  

7.  Three  tenths  of  40  are  

8.  Seven  tenths  of  20  are  


.2  of  20  =: 

.2  of  30  = 
.2  of  40  = 
.2  of  50  = 

.4  of  20  = 
.4  of  30  = 
.4  of  40  = 
.6  of  20  = 


9.  .1  of  24  is - 

10.  .1  of  32  is 

11.  .1  of  43  is - 

12.  .1  of  23  = 

13.  .1  of  12  = 

14.  .1  of  33  = 

15.  .1  of  42  = 


and  — 
and  — 
and  — 

.2  of  23 

.2  of  12 
.2  of  33 
.2  of  42 


tenths, 
tenths, 
tenths. 


.2  of  24 
.2  of  32 

.2  of  43 


.3  of  23 
.3  of  12 
.3  of  33 
.3  of  42 


16.  1  tenth  of  240  = 
17.1  tenth  of  250  = 

18.  1  tenth  of  225  = 

19.  1  tenth  of  235  = 


(a)  Find  .2  of  240. 

(b)  Find  .2  of  250. 

(c)  Find  .2  of  225. 

(d)  Find  .2  of  235c 


(e)  Add  $324.2,  $123.1,  and  $231.3. 

(f)  Add  $140.4,  $203.2,  and  $132.2. 

(g)  Add  $222.2,  $101.1,  and  $303.3. 
■(h)  Add  $158.2,  $300.2,  and  $121.3. 
(i)  Add  $325.8,  $234.3,  and  $286.6. 
(j)  Add  $165.5,  $248.4,  and  $244.4. 


?^  -^r  >>rrvT%i£T'   x^rrgfyimnr^ 


-3V     - 

5»  2?  :ci- 


:!  if  t:^ 


.f  $^  ^ 

if  SiS  5?  .       —  '~2t  %>  — 

_   ^  *    it-    '-iL   ^ »    — 


(r      _-^    45^  


3  'C'f  2  in,.  — 


13-  Six  Ter^5  :f  f^  =  .7  :z  f  i:  = 

14-  SixT.Ti-         : T-=  .7'j^2i:i    = 


7-i  i^    f  To. 

mil  _  :z  ^- 


G£  lo. 


_  .  >  GE  :fr5- 


16? 


JL^ TEJTTME. 


1.     .? 


2. 

^. 

3. 

V  — 

4. 

5. 

?2r' 

6. 

jd  ' 

7. 

?:^ 

8. 

-$_- 

feid  .1  •'"£  ?f5--" .      '     '  ^  i 


j^  ^^  ^-xTt, 


9.  $6  X  J-  "-_^-.  fni  :  -.-Til  ^Gii  $^. 


10.   ?' 

11.  t^ 

12.  $S 


A  ,-;^  iS>.= 


13.  >  =  ^  ^  =  f 

14.  >_.         1  =  ^:1  X  J  =  |1Z 

15.  .?-   ..:  -2  =  #7   *    .5  ^  f  14 


.  _.»j-        JJ^       -7--:,7!T 


m 


16.   |2         -  ^     - 


18.  i:.      -      _    _.   11^  X  ±.  - 

-S12  X  2,4  = 


»  e  »  1-  ^    -  -     T  4.  :     ^  -  _4  X  -4. 


164                       ELEMENTARY    ARITHMETIC. 
DECIMALS TENTHS. 

1.  Multiply   $275  by  2.3.     This   means,  >i6^ 
tioo  times  $27 5  lolus  three  tenths  of  $27S. 

Operation  No.  1.  Explanation. 

^275  Two  times  $275  are  $550. 


2.3 


One  tenth  of  $275  is  $27.5. 
Three  tenths  of  $275  are  $82.5. 


$550.      (2  times  $275.)      $550  +  $82.5  =  $632.5. 
1.5    (.3  of  $275.) 


$632.5    (2.3  times  $275.) 


Operation  No.  2.  Explanation. 

1275^  One  tenth  of  $275  is  $27.5. 

Three  tenths  of  $275  are  $82.5. 
Two  times  $275  are  $550. 


2.3 


$82.5    (.3  of  $275.)  1550  +  $82.5  :::.  $632.5. 

$550.       (2  times  $275.) 

$632.5    (2.3  times  $275.) 

SUGGESTED    NUMBER    STORY. 

If  one  acre  of  land  is  worth  $275, 
1  tenth  of  an  acre  is  worth  — 


3  tenths  of  an  acre  are  worth 

2  acres  are  worth  . 

2.3  acres  are  worth  . 


(a)  Multiply  $245  by  2.3.      (b)  $146  x  2.3  = 
(c)  Multiply  $234  by  3.2.      (d)  $156  x  3.2  = 

(e)  Divide  25.8  by  .2.         (f )  Divide  37.6  by  .2. 
(g)  Divide  36.5  by  .5.        (h)  Divide  48.5  by  .5. 


PART  III.  165 

DECIMALS TENTHS. 

1.  Victor  lives  3.4  miles  north  of  the  Court 
House;  Harry  lives  2.3  miles  south  of  the  Court 
House ;  from  Victor's  home  to  Harry's  home  it  is 
miles. 

(a)  William  lives  27.4  miles  north  of  Wauke- 
gan;  Henry  lives  46.5  miles  south  of  Waukegan. 
How  far  is  it  from  William's  home  to  Henry's 
home  ? 

2.  Mr.  Dow  lives  2.4  miles  west  of  Chicago; 
Mr.  Just  lives  5.6  miles  west  of  Chicago;    from 

Mr.  Dow's   home  to   Mr.  Just's  home  it  is  

miles. 

(b)  Mr.  Jones  lives  24.3  miles  west  of  Chicago; 
Mr.  Adams  lives  51.7  miles  west  of  Chicago.  How 
far  is  it  from  Mr.  Jones's  home  to  Mr.  Adams's 
home  ? 

3.  Jane  lives  2.4  miles  south  of  the  Chicago 
post-office;  Helen  lives  3.5  miles  south  of  Jane's 
home;  from  the  Chicago  post-office  to  Helen's 
home  it  is  miles. 

(c)  Mrs.  Smith  lives  17.3  miles  south  of  the 
Chicago  post-office;  Mrs.  Brown  lives  24.5  miles 
south  of  Mrs.  Smith's  home.  How  far  is  it  from 
the  Chicago  post-office  to  Mrs.  Brown's  home? 

(d)  Divide  75.8  by  2.  (e)  Divide  85.6  by  2. 
(f )  Divide  46.5  by  5.  (g)  Divide  94.5  by  5. 
(h)  Divide  61.5  by  5.     (i)  Divide  56.5  by  5. 


166                       ELEMENTARY    ARITHMETIC. 
DECIMALS TENTHS. 

1.  Sarah  paid   $1.2  for  some  books  that  cost 

$.3  each;   there  were  books.      I  found  the 

number  of  books  that  Sarah  bought  by  finding  how 
many  times  $.3  is  contained  in  $1.2.  $.3  is  con- 
tained in  $1.2 times.  Show  upon  the  black- 
board how  this  would  appear  as  an  example  in 
division. 

$.4)$1.6         $.2)$2.4         $.2)$4.6         $.5)$7.5 

(a)  Sarah's  mother  paid  $27.6  for  some  chick- 
ens that  cost  $.3  each.  How  many  chickens  did 
she  buy?  I  can  find  the  number  of  chickens  by 
finding  how  many  times  — . 

2.  John  paid  $1.2  for  3  second  readers;  each 

reader    cost   .     I    found   the    cost    of    1 

reader  by  finding  1  of  $1.2.    ^  of  $1.2  is . 

Show  upon  the  blackboard  how  this  would  appear 
as  an  example  in  division. 

4)$1.6  2)$2.4  2)$4.6  5)$7.5 

(b)  John's  father  paid  $34.5  for  3  tons  of  hay. 
How  much  did  one  ton  cost?  I  can  find  the  cost 
of  one  ton  by  finding  — -. 

(c)  Add  421.6,  135.3,  and  264.5. 

(d)  Add  142.6,  25.4,  and  391.5. 

(e)  Add  204.6,  48.3,  and  162.7. 


PART  III.  167 

DECIMALS TENTHS. 

1.  Henry  paid  $4  for  some  young  clucks  at  $.2 
each ;  there  were  ducks.  I  found  the  num- 
ber of  ducks  that  Henry  bought  by  finding  how 
many  times  .  Show  upon  tlie  black- 
board how  this  woukl  appear  as  an  example  in 
division. 

$.2)$6.Q    $.4)$8.Q    $.2)$10.    $.5)$1Q.   $.2)$8. 

(a)  Henry's   father   paid    $48    for  some   fence 
posts  that  cost  $.2  each.     How  many  posts? 

2.  Jane  paid  $6  for  4  yards  of  velvet;   each 

yard  cost  .    I  found  the  cost  of  one  yard 

by  finding  J  of  .  Show  upon  the  black- 
board how  this  would  appear  as  an  example  in 
division. 

2)$5.Q        4)$1Q.Q         2)$7.         2)$9.        4)$2. 

(b)  Jane's    mother   paid    $26    for    4    curtains. 
How  much  did  one  curtain  cost? 

(c)  Mr.  Curtis  paid  $17  for  5  barrels  of  flour. 
How  much  did  one  barrel  cost? 

(d)  If  two  acres  of  land  are  worth  $175,  how 
much  is  one  acre  worth? 

(e)  From  124.2  subtract  18.5. 

(f)  From  135|  subtract  112.1. 

(g)  From  1641  subtract  122.4. 
(h)  From  298f  subtract  175.7. 


168  ELEMENTARY    ARITHMETIC. 

DECIMALS TENTHS. 

1.  William  paid  $2.3  for  a  pair  of  shoes;  at 

the  same  rate  3  pairs  of  shoes  would  cost . 

I  found  the  cost  of  3  pairs  by  multiplying  


.     Show  upon  the  blackboard  how  this 

would  appear  as  an  example  in  multiplication. 

$2.3            $3.4             $2.5             $3.5            $6.2 
2  2  2  2  3 

(a)  William's  father  paid  $36.5  for  a  cow.     At 
the  same  rate,  how  much  would  3  cows  cost  ? 

2.  Mary  paid  $1.5  for  3  dozen  oranges;  one 

dozen  oranges  cost  .     I  found  the  cost 

of  one  dozen  by  finding  .     Show 

upon  the  blackboard  how  this  would  appear  as  an 
example  in  division. 

5)$2.5       4)$1.6       3)$1.8       2)$6.4       2)$5.4 

(b)  Mary's    mother   paid    $27.5    for    5    chairs. 
How  much  did  one  chair  cost  ? 

(c)  Multiply  $325  by  2.2. 

(d)  Multiply  $124  by  1.3. 

(e)  Multiply  $426  by  3.4. 

(f)  Multiply  $321  by  3.4. 

(g)  Multiply  $347  by  4.3. 
(h)  Multiply  $252  by  4.3. 
(i)  Multiply  $212  by  1.5. 
(j)  Multiply  $140  by  2.1. 


PART  III.  169 


DECIMALS TENTHS. 


1.  Alice  paid  $2.5  for  ribbon  that  cost  $.5  a 
yard;  she  bought  yards.  I  found  the  num- 
ber of  yards  by  finding  -.     Show  upon 

the  blackboard  how  this  would  appear  as  an  ex- 
ample in  division. 

|.5)$2.5  $.3)$1.8   $.2)$3.6   $.2)$5.2  $.2)$4.6 

(a)  Alice's  mother  paid  $27.6  for  a  carpet  that 
cost  $.6  a  yard.     How  many  yards  did  she  buy? 

2.  Peter  paid  $1.3  for  a  hat;  at  the  same  rate 

3  hats  would  cost  .     I  found  the  cost  of 

of  3  hats  by  multiplying  .     I  could 

find  the  cost  of  4  hats  by  multiplying  • . 

Show  upon  the  blackboard  how  these  would  appear 
as  examples  in  multiplication. 

$2.4        $2.5         $2.6         $2.7         $2.8        $2.9 
2  2  2  2  2  2 


(b)  Peter's  father  paid   $74.6  for  a  horse;    at 
the  same  rate  how  much  would  4  horses  cost? 

(c)  Divide  28.8  by  .4.  (d)  Divide  29.6  by  .4. 
(e)  Divide  37.5  by  .5.  (f )  Divide  62.5  by  .5. 
(g)  Divide  25.2  by  .6.     (h)  Divide  26.4  by  .6. 


170                       ELEMENTARY    ARITHMETIC. 
DECIMALS TENTHS. 

1.  Mr.  Brown  had  1.8  acres  of  land  which  he 
divided  into  lots,  each  containing  .3  of  an  acre; 

there  were  lots.     I  found  the  number  of  lots 

by  finding  .     Show  upon  the  blackboard 

how  this  would  appear  as  an  example  in  division. 

.3  of  an  acre)  1.5  acres  5  of  an  acre) 3. 5  acres 

.4  of  an  acre) 2. 4  acres  .6  of  an  acre) 4. 2  acres 

(a)  Mr.  Lyon  had  46.8  acres  of  land  which  he 
divided  into  lots,  each  containing  .3  of  an  acre. 
How  many  lots  ? 

2.  Mr.  Nichols  had  1.8  acres  of  land  which  he 
divided  into  3    equal   parts ;    each   lot   contained 

^ .     I  found  the  amount  of  land  in  each 

lot  by  finding  .  Show  upon  the  black- 
board how  this  would  appear  as  an  example  in 
division. 

3)1.5  acres    5)3.5  acres     4)8.4  acres     3)6.6  acres 

(b)  Mr.  Toll  had  48.6  acres  of  land  which  he 
divided  into  three  equal  lots.  How  many  acres  in 
each  lot  ? 

(c)  Divide  24.8  by  4.  (d)  Divide  25.2  by  4. 
(e)  Divide  36.5  by  5.  (f)  Divide  38.5  by  5. 
(g)  Divide  47.6  by  4.  (h)  Divide  51.2  by  4. 
(i)  Divide  39.5  by  5.  (j)  Divide  42.5  by  5. 


PART  III.  171 

DECIMALS TENTHS. 

1.  Robert  had   $1.2;    Peter  liad   ^   as  much; 
Peter  had  . 

(a)  Mr.  Ford  had  $64.2;  Mr.  Davis  had  I  as 
much.     How  much  money  did  Mr.  Davis  have? 

2.  Mr.  Frank's  hat  cost  $1.2;    this  was  1  as 

much  as  his  coat  cost;  his  coat  cost  .     They 

both  cost  . 

(b)  A  harness  cost  $24.5;  this  was  1  as  much 
as  a  horse  cost.  How  much  did  the  horse  cost? 
How  much  did  both  together  cost? 

3.  Alice's  hat  cost  $1.2;  her  gloves  cost  f  as 
much;  her  gloves  cost  ;    both  together  cost 


(c)  Mr.  Pratt's  buggy  cost  $136.5;  his  horse 
cost  f  as  much.  How  much  did  his  horse  cost? 
How  much  did  both  together  cost? 


'&' 


4.  Verne's   gloves   cost    $1.2;    this  was  f  as 

much  as  her  hat  cost;    her  hat  cost  ;    both 

together  cost  . 

Mrs.  Hill's  new  curtains  cost  $85.4;  this  was  f 
as  much  as  her  carpets  cost. 

(d)  How  much  did  the  carpets  cost? 

(e)  How  much  did  both  together  cost? 

(f)  Add  27.4,  36.3,  25.7,  and  13.2. 

(g)  Add  12.5,  14.2,  15.3,  and  10.2. 
(h)  Add  22.2,  33.3,  44.4,  and  55.5. 


172                       ELEMENTARY    ARITHMETIC. 
DECIMALS TENTHS. 

1.  If  2  bushels  of  wheat  are  worth  $1.6,  3 
bushels  of  wheat  are  worth  . 

(a)  If  2  tons  of  bran  are  worth  $28.8,  how 
much  are  3  tons  of  bran  worth  ? 

2.  If   3   bushels  of  apples  are  worth   $1.8,  2 
bushels  of  apples  are  worth  . 

(b)  If  3  tons  of  oil  meal  are  worth  $73.5,  how 
much  are  2  tons  of  oil  meal  worth  ? 

3.  If  3  bushels  of  corn  are  worth  $1.2,  4  bush- 
els of  corn  are  worth  . 

(c)  If  3  tons  of  nails  are  worth  $106.5,  how 
much  are  4  tons  of  nails  worth? 

4.  $60   X    .2  =  (d)  $740  X    .2  = 

5.  $63   X    .2  =-  (e)  $745   x    .2  = 

6.  $5.4  X  2     :=  (f)  $83.6  x  2     = 

7.  $50   X  2.2  =  (g)  $840   x  2.2  =: 

8.  $55   X  2.2  =  (h)  $635   x  4.2  = 

9.  $2.7 -$.9::=  (i)  $65.2  X  $.4  = 

10.  If  4  lbs.  of  coffee  are  worth  $1.6,  5  lbs.  of 
coffee  are  worth  . 

(j)  If  4  acres  of  land  are  worth  $97.2,  how 
much  are  7  acres  worth? 

(k)  If  5  tons  of  hay  are  worth  $62.5,  how  much 
are  6^  tons  worth? 

(1)  From  641.3  subtract  238.1. 
(m)  From  524.7  subtract  161.4. 


PART    III. 


173 


SIMPLE    NUMBERS. 


1.  At 

2.  At 

3.  At 

4.  At 

5.  At 

6.  At 

7.  At 

8.  At 

9.  At 

10.  At 

11.  At 


$23  each 
$25  each 
$28  each 
$27  each 
$23  each 
$24  each 
$25  each 
$23  each 
$25  each 
$27  each 
$24  each 


45 
23 


135 
90 

1035 


(a) 


(3  times  45.) 
(20  times  45.) 

(23  times  45.) 


461 
23 


138 

92 

10694 


2  cows 
10  cows 
10  cows 
10  cows 
20  cows 
20  cows 

20  cows 

22  cows 

23  cows 

21  cows 

24  cows 


cost 
cost 
cost 
cost 
cost 
cost 
cost 
cost 
cost 
cost 
cost 


dollars, 
dollars, 
dollars, 
dollars, 
dollars, 
dollars, 
dollars, 
dollars, 
dollars, 
dollars, 
dollars. 


(b)  Multiply  48  by  24 

(c)  Multiply  37  by  46 
(d)Multiply  58by  35 

(e)  Multiply  72  by  21 

(f )  Multiply  86  by  24 


(g) 


(23  times  ^.) 
(3  times  46.) 
(20  times  46.) 

(23  times  46f) 


46.5 
23 


139.5 

930. 

1069.5 


(1^) 


(3  times  46.5.) 
(20  times  46.5.) 

(23  times  46.5.) 


(i)  Multiply  47i  by  25.  (j)    47.5  by  25. 

(k)  Multiply  38i  by  23.  (1)    38.5  by  23. 


174  ELEMENTARY    ARITHMETIC. 

DENOMINATE    NUMBERS. 

1.  I  can  reduce  (change)   6  quarts  1  pint  to 
pints.     6  qt.  1  pt.  =  pints. 

(a)  Reduce  36  qt.  1  pt.  to  pints. 

2.  I  can  reduce  3  gal.  2  qt.  to  quarts.     3  gaL 
2  qt.  =  quarts. 

(b)  Reduce  36  gal.  2  qt.  to  quarts. 

3.  I  can  reduce  2  ft.  5  in.  to  inches.     2  ft.  5 
in.  =  inches. 

(c)  Reduce  23  ft.  5  in.  to  inches. 

4.  I  can  reduce  (change)  15  pints  to  quarts. 
15  pints  — 

(d)  Reduce  85  pints  to  quarts.      2)85 

5.  I  can  reduce  15  quarts  to  gallons.    15  qt.  = 

(e)  Reduce  177  quarts  to  gallons.  4)177 

6.  I  can  reduce  21  pecks  to  bushels.     21  pk.  = 

(f )  Reduce  230  pecks  to  bushels.  4)230 

7.  I  can  reduce  18  days  to  weeks.      18  days  = 

(g)  Reduce  365  days  to  weeks. 

8.  I  can  reduce  2  hours  20  minutes  to  minutes. 
2  hours  20  minutes  =  minutes. 

(h)  Reduce  7  hours  20  minutes  to  minutes. 

(i)  Divide  $326  by  $5.  (j)  Divide  $427  by  $5. 
(k)  Divide  $561  by  $5.  (1)  Divide  $472  by  $5. 
(m)Divide  $358  by  $5.   (n)  Divide  $629  by  $5. 


PART  III.  175 

COMMON    FRACTIONS. 

1.  One  half  is  fourteenths. 

2.  One  seventh  is  fourteenths. 

3.  Two  sevenths  are  —  fourteenths. 

4.  Three  sevenths  are  fourteenths. 

5.  One  half  and  1  fourteenth  are . 

6.  One  half  less  2  fourteenths  are . 


7.  Two  sevenths  and  1  fourteenth  are 

8 .  Two  sevenths  less  1  fourteenth  are  ■ 

9 .  Three  sevenths  and  1  fourteenth  are 

10.  Three  sevenths  less  1  fourteenth  are 

11.  -J-  +  -^\,  means  .     ^  and  -j\-  = 

12.  4"  —  fV?  i^eans  .     -J-  l^ss  fV  = 

13.  -f-  X  5,  means  .       5  times  |-  = 

14.  14  X  -f,  means  .     |^  of  14  = 

15.  14  X  2f,  means  ■.  2f  times  14  = 

16.  I-  -=-  -A ,  means  .     -A-  is . 


17.  2 

18.  1 


i,  means  — .       ^  is 

2,  means  .       i  of  4- 


19.  $1.4  is  I  of  .  I  of  1.5  = 

(a)  $36.8  is  |  of  how  many  dollars? 

(b)  I  of  36.6  3^ 
(c)  $54.2  is  I  of  how  many  dollars? 

(d)  I  of  55.2  = 
(e)  $17.4  is  I  of  how  many  dollars? 

(f)  I  of  18.6  = 

(g)  Divide  $476  by  5.       (h)  Divide  $397  by  5. 
(i)  Divide  $623  by  5.       (j)  Divide  532  by  5. 


176  ELEMENTARY   ARITHMETIC. 

COMMON    FRACTIONS. 

1 .  Add  I  and  |.     (4  =  ^^,     |  =  ^^.) 

2.  Add  I  and  |.      (Change  |  to  ^.) 

3.  From  4  subtract  -|-.     (i.  =  j^.     ^  =  j^.) 

4.  From  ^  subtract  -J-.      (Change  1  to  ^g.) 

5.  Multiply  6  by  5|.      (5  times  6,  plus  |  of  6.) 

6.  Multiply  84-  by  6.      (6  times  J,  plus  6  times  8.) 

7.  Divide  ^  by  7.     (Find  \  of  f ) 

8.  Divide  4  by  f.      (Find  how  many  times,  etc.) 

9.  Find  the  sum  of  2.4  and  1|^.     (}  =  ^^.) 

10.  Find  the  sum  of  S^-  and  2^^.     (^  =  ^^.) 

11.  Find  the  difference  of  3|  and  1.3.     (|  -  ^.) 

12.  Find  the  difference  of  4|  and  2yV'    (^  =  xr) 

13.  Find  the  product  of  8  multiplied  by  4|-. 

14.  Find  the  product  of  4f  multiplied  by  8. 

15.  Find  the  quotient  of  |-  divided  by  2. 

16.  Find  the  quotient  of  2  divided  by  f. 


17. 

1  4_  1     1    1  _  ? 

(i 

—    6"-        i-    —    G*) 

18. 

1   4_  1     1       1     _  ? 

a- 

—  T2-        4    —  T3".) 

19. 

1     1     1     1     1    —  ? 
-2  ^  "3   T^  T  —    • 

tt^ 

=  T-^,  etc.) 

20. 

1     1     1     1     1    _  ? 

ih- 

=  8,  etc.) 

(a)  Add  146|,  125|,  and  136|. 

(b)  Add  224.5,  126|,  and  275. 

(c)  Add  375,  246,  233,  and  145. 


PART  III.  177 

MISCELLANEOUS    PROBLEMS    IN    FRACTIONS. 

1.  3  inches  are  contained  in  7  inches  and 

— times. 


6-^3=  7-3=  8-3  = 

2.  3  tenths  are  contained  in  7  tenths  — 


.6  -^  .3  =         .7  -  .3  =         .8  -  .3  = 
3.  3  fourteenths  are  contained  in  7  fourteenths 


6.3_  7.3_  8^3_ 

TT  ~  TT  —  TT    •    TT  —  XT    *    TT  — 

4.  4  inches  are  contained  in  9  inches and 

times. 


8^4=         9-4=         10-4=         11-4  = 
5.  4  tenths  are  contained  in  9  tenths 


.8 -.4=       .9 -.4=       1.0 -.4=       1.1 -.4  = 

6.  4  twelfths  are  contained  in  9  twelfths 

8.4—  9      _:^      4      _         XQi  _:_  _4_  —         IJL  ^  _4__  _ 

1-2   ~  T2   ~        Tl^     •      1  2    —  12-12—  12-12    — 

7.  One  half  of  6  is  1  third  of  . 

8.  One  third  of  6  is  1  half  of  . 

9.  One  fourth  of  8  is  1  half  of  . 

10.  One  fourth  of  8  is  1  third  of  --, 

11.  One  half  of  8  is  1  third  of  , 


(a)  From  432  subtract  271|. 

(b)  From  536  subtract  362.4. 

(c)  From  375  subtract  28|. 

(d)  From  621  subtract  206.3. 


178  ELEMENTARY    ARITHMETIC. 

MEASUREMENTS. 

1.  A  rectangle  1   inch  wide  and   1  foot  long 
contains  square  inches. 

2.  A  rectangle  2  inches  wide  and  1  foot  long 
contains  square  inches. 

3.  A  rectangle  3  inches  wide  and  1  foot  long 
contains  square  inches. 

4.  A  rectangle  8  inches  wide  and  1  foot  long 
contains  square  inches. 

5 .  A  12-incli  square  contains square  inches. 

6.  A  12-inch  square  is  a  square  foot. 

7.  An  oblong  2  feet  by  3  feet  contains  . 

8.  An  oblong  1  foot  by  5  feet  contains  . 

9.  A  square  foot  is  what  part  of  a  2-foot  square  ? 

10.  2  square  feet  are  what  part  of  a  2-foot  square  ? 

11 .  3  square  feet  are  what  part  of  a  2-foot  square  ? 

12.  12  square  inches  are  what  part  of  a  square 
foot? 

13.  24  square  inches  are  what  part  of  a  square 
foot? 

14.  An  oblong  3  inches  wide  and  1  foot  long  is 

of  a  square  foot. 

15.  An  oblong  4  inches  wide  and  1  foot  long  is 

of  a  square  foot. 


16.  An  oblong  6  inches  wide  and  1  foot  long  is 
of  a  square  foot. 

(a)  Multiply  $26  by  24.       (d)  $28  x  6.5. 

(b)  Multiply  $26  by  24i.     (e)  $34  x  25. 

(c)  Multiply  $28  by  6i.       (f)  $34  x  2.5. 


PART  III.  179 

ME  AS  UREMENTS . 

1.  A  rectangle  1  ft.  wide  and  1  yd.  long  con- 
tains    square  feet. 

2.  An  oblong  2  ft.  wide  and  1  yard  long  con- 
tains    square  feet. 

3.  A  3-foot  square  contains  square  feet. 

4.  A  3-foot  square  is  a  square  ijard. 

5.  An  oblong  1  yd.  by  3  yd.  contains  . 

6.  An  oblong  2  yd.  by  3  yd.  contains  . 

7.  A  square  foot  is of  a  sq.  yd. 

8.  Two  square  feet  are of  a  sq.  yd. 

9.  Three  square  feet  are of  a  sq.  yd. 

10.  Six  square  feet  are  of  a  sq.  yd. 

11.  A  2-foot  square  is  of  a  sq.  yd. 

12.  A  2-incli  square  is  — •- —  —  of  a  3-incli 

square. 

13.  A  2-incli  square  is  —  of  a  4-inch 

square. 

14.  A  1-inch  square  is  of  a  2-inch 

square. 

15.  A  1-inch  square  is of  a  3-mch 

square. 

16.  A  1-inch  square  is  — '■ of  a  4-inch 

square. 

17.  The  area  of  an  oblong  1  foot  wide  and  5  feet 
long  is of  a  square  yard. 

(a)  Divide  $342  by  $6.   (b)  Divide  $343  by  $6. 
(c)  Divide  $276  by  $6.   (d)  Divide  $278  by  $6. 


180 


ELEMENTARY    ARITHMETIC. 


RATIO    AND    PKOPORTIOlSr. 


5*7^ 


10  cents. 


1.  If  3  apples  are  worth  5  cents,  6  apples  are 
worth  cents. 


3. 


4. 


[  3  is 
5  is 

4  is 
20  is 

)  is 

[12  is 


of  6.  6  is 

of  10.  10  is 

of  12.  12  is 

of  60.  60  is 

of  20.  20  is 

of  48.  48  is 


times  3. 
times  5. 

times  4. 
times  20. 

times  5. 
times  12 


5.  If  25^  pays  for  7  lemons,  50^  pays  for 

6.  If  10^  pays  for  3  oranges,  30^  pays  for 

7.  If  $20  pays  for  3  tons,  $80  pays  for  - 


8.  If  50^  pays  for  4  gallons,  25^  pays  for 

9.  If  80^  pays  for  12  tickets,  20^  pays  for 

10.  If  75^  pays  for  9  rides,  25^  pays  for . 

11.  Mary  has  10^;  Jane  has  20^;  if  Mary  can 
buy  3  pencils,  Jane  can  buy  pencils. 

12.  Harry  has  50^;    Alice  has  25^;    if  Harry 


can  buy  6  tablets,  Alice  can  buy 


tablets. 


(a)  Divide  $342  by  6.  (b)  Divide  $344  by  6. 
(c)  Divide  $277  by  6.  (d)  Divide  $279  by  6. 
(e)  Divide  $445  by  6.       (f )  Divide  $447  by  6. 


PART  III.  181 


RATIO    AXD    PROPORTION. 


1.  Twelve  oranges   are  'worth  times  as 

much  as  6  oranges.     If  6  oranges  are  worth  11^, 
12  oranges  are  worth  — cents. 

2.  Six  Readers  are  worth  times  as  much 

as  2  Eeaders.     If  2  Readers  are  worth  $1.20,  6 
Readers  are  worth  . 

3.  Five  dozen  eggs   are  w^ortli as 

much  as  10  dozen  eggs.     If  10  dozen  are  worth 
$2.20,  5  dozen  are  worth  . 


4.  Five  yards  of  velvet  are  worth 

as  much  as  15  yards  of  velvet.     If  15  yards  are 
worth  $12,  5  yards  are  worth  dollars. 

5.  If  6  oranges  are  worth  9^,  2  oranges  are 
Avorth  cents. 

6.  If  3  tons  of  coal  are  worth  $20,  6  tons  are 
worth  dollars. 

7.  John  earns  $7  in  2  weeks;   in  6  weeks  he 
earns  dollars. 

8.  If  3  acres  of  land  yield  5  tons  of  hay,  at  the 
same  rate  9  acres  will  yield tons. 

9.  If  20  lbs.  of  salt  cost  12^,  at  the  same  rate 
40  lbs.  will  cost  cents. 

10.  If  5  yards  of  ribbon  cost  I  of  a  dollar,  at 
the  same  rate  15  yards  will  cost  . 

(a)  Add  274|,  342,  and  125^^- 

(b)  Add  145fV,  231,  and  273|. 

(c)  Add  224,  375,  432,  and  227. 


182  ELEMENTARY    ARITHMETIC. 

MISCELLANEOUS    PROBLEMS. 

1.  In  1^  liours  there  are  minutes. 

(a)  How  many  minutes  in  T^-  hours? 


2.  Henry  earns  $34^  each  week;  in  6  weeks  he 
earns  dollars. 

(b)  How  many  dollars  does  Henry  earn  in  52 
weeks  ? 

3.  James  spent  ^  of  the  money  his  father  gave 
him  for  a  slate  and  |^  of  it  for  a  book,  and  had  10^ 

left.     Before  he  spent  any  money  he  had  

cents. 

(c)  A  man  spent  -|-  of  l^is  month's  wages  for 
fuel  and  ^  of  it  for  groceries  and  had  $12.5  left. 
How  much  was  his  wages? 

4.  At  ^  of  a  dollar  a  yard,  10  yards  of  ribbon 
cost  dollars. 

(d)  At  ^  of  a  dollar  a  yard,  how  much  will  155 
yards  of  ribbon  cost? 

5 .  Alice  spent  i  of  her  money  and  had  8^  left ; 

before  spending  any  money  she  had  cents; 

she  spent  cents. 

(e)  Alice's  mother  spent  |-  of  her  money  and 
had  $73  left.  How  much  money  had  she  before 
spending  any?     How  much  did  she  spend? 

(f)  From  1624  subtract  902-|-. 

(g)  From  2436  subtract  814.3. 


PART  III.  183 

SIMPLE    NUMBERS. 

(a)                  (b)  (c)  (d) 

12  dollars         15  oranges  25^  275 

5  dollars           6  oranges  8^  146 

7  dollars           9  oranges  17^  129 

the 


1.  In  problem  (a)  the  minuend  is 
subtrahend  is  ;  the  difference  is  — 

2.  In  problem  (b)  the  subtrahend  is 
minuend  is  ;  the  difference  is  — — 


3.  In  problem  (c)  the  difference  is 
minuend  is  ;  the  subtrahend  is  — 

4.  In  problem  (d)  the  minuend  is 
difference  is  ;  the  subtrahend  is  — 


5.  In  a  problem  the  minuend  is  8  dollars 


the 
the 
the 

the 


subtrahend  is   5   dollars    ;    the   difference  is 


6.  When  the  difference  is  5  inches  and  the  sub- 
trahend is  4  inches,  the  minuend  is — . 

7.  When  the  difference  is  11  feet  and  the  min- 
uend is  14  feet ,  the  subtrahend  is . 

8.  The  sum  of  two  numbers  is  15;  one  of  the 
.numbers  is  6 ;  the  other  number  is  . 

9.  The  difference   of  two  numbers  is   9;    the 
larger  number  is  20 ;  the  smaller  number  is  . 

(e)  Multiply  $542  by  3.  (f)  $542  x  .4. 

(g)  Multiply  $542  by  3.4.       (h)  $542  x  3.5. 
(i)  Multiply  $542  by  3^.        (j)  $542  x  2 J. 


184  ELEMENTARY    ARITHMETIC. 


DENOMINATE    NUMBERS. 

1.  2  gal.  1  qt.  +  3  gal.  2  qt.  are 


(a)  Add  47  gal.  1  qt.  and  35  gal.  2  qt. 
2.  2  bu.  3  pk.  -f  3  bu.  3  pk.  are 


(b)  Add  54  bu.  3  pk.  and  29  bu.  3  pk. 
3.   6  gal.  3  qt.  —  3  gal.  1  qt.  are 


(c)  From  45  gal.  3  qt.  subtract  37  gal.  1  qt. 

4.  4  gal.  1  qt.  —  1  gal.  3  qt.  are  

(d)  From  57  gal.  1  qt.  subtract  24  gal.  3  qt. 

5.  3  bu.  2  pk.  X  4  equals  . 

(e)  Multiply  27  bu.  2  pk.  by  6. 

6.  3  bu.  2  pk.  -^  2  pk.  equals  — — . 

(f )  Divide  12  bu.  2  pk.  by  2  pk. 

7.  4  bu.  2  pk.  -^  2  equals 


(g)  Divide  84  bu.  2  pk.  by  2. 

8.  Six  yards  2  feet  equal  feet. 

(h)  Reduce  45  yards  1  foot  to  feet. 

9.  Two  pecks  3  quarts  equal  quarts. 

(i)  Reduce  23  pecks  3  quarts  to  quarts. 

10.  Twenty-seven  feet  equal  yards. 

(j)  Reduce  56  feet  to  yards. 

(k)  Divide  $245  by  $7.  (1)  $246  -  $7  : 
(m) Divide  $252  by  $7.  (n)  $254  -  $7  : 
(o)  Divide  $364  by  $7.        (p)  $367  -  $7  : 


PART  III.  185 

COMMOX    FRACTIONS. 

1.  One  third  is  fifteenths. 

2.  One  fifth  is fifteenths. 

3.  Two  fifths  are  fifteenths. 

4.  Three  fifths  are  fifteenths. 

5.  One  third  and  1  fifteenth  are  . 

6.  One  third  less  1  fifteenth  are  . 

7.  Two  fifths  and  1  fifteenth  are  . 

8.  Two  fifths  less  1  fifteenth  are  — . 

9.  Three  fifths  and  2  fifteenths  are . 

10.  Three  fifths  less  2  fifteenths  are  . 

11-  i  +  tV.  means  ^.      i  +  yV  = 

12.  I  -  ^\,  means .       |  -  A  = 

13.  "I  X  8,  means  .         8  times  -|  = 

14.  10  X  I,  means .      -|  of  10  = 

15.  10  X  2|,  means  ^^ .    2|-  times  10  = 

16-  I  -^  iV ?  means  .      -^^  is  . 

17.  3  -^  f ,  means  .         f  are — . 

18.  f  ^  3,  means .        ^  of  f  = 


19.  At  $10  an  acre,  21  acres  of  land  cost  . 

(a)  At  $65  an  acre,  how  mnch  will  2^  acres  of 
land  cost? 

20.  One  half  of  the  month  of  November  plus 
one  fifteenth  of  the  month  equals  days. 

(b)  Divide  $364  by  7.  (c)  $365  -  7  = 
(d)  Divide  $161  by  7.  (e)  $165  -  7  = 
(f)  Divide  $455  by  7.         (g)  $459  -  7  - 


186  ELEMENTARY    ARITHMETIC. 

COMMON    FRACTIONS. 

1.  Add  f  and  4.  (1  =  ^^.    1  =  -^.) 

2.  Add  I  and  -^.       (Change  |  to  ^^.) 

3.  From  |^  subtract  |.  (f  =  t^.    1  =  y^.) 

4.  From  y^^  subtract  \.        (Change  i  to  — .) 

5.  Multiply  8  by  3  J.     (3  times  8,  plus  J  of  8.) 

6.  Multiply  5|-  by  6.      (6  times  i,  plus  6  times  5.) 

7.  Divide  |  by  5.  (Find  1  fifth  of  f.) 

8.  Divide  5  by  |.  (Find  how  many  times,  etc.) 

9.  Find  the  sum  of  3.2  and  If.       (f  =  ^^.) 

10.  Find  the  sum  of  2|  and  2/^.      (1  =  y-^.) 

11.  Find  the  difference  of  Sf  and  1.2. 

12.  Find  the  difference  of  4  J-  and  2^-^, 

13.  Find  the  product  of  10  multiplied  by  3f. 

14.  Find  the  product  of  3|-  multiplied  by  10. 

15.  Find  the  quotient  of  4  divided  by  3. 

16.  Find  the  quotient  of  3  divided  by 


5* 


17. 

1  4-  i  4-    1     —  ? 

(3^  =  T^- 

1 

18. 

1     1     1   4_    1     —  ? 

(i  —  T¥' 

1 

T 

19. 

1    J-    1    -U     1      —  ? 

(i  =  To"* 

1 

20. 

2    _l_    2      1        1      _  ? 

2 
■5 

=  T0-) 
=  TT-) 


(a)  Add  254|,  325,  and  243J. 

(b)  Add  324|,  271,  and  442|-. 

(c)  Add  462,  575,  834,  926. 
(d)Add378,  246,  575,  242. 


PART  III.  187 

MISCELLANEOUS    PROBLEMS    IN    FRACTIONS. 

1.  Acid  I,  4"?  ^^cl  yV-  (Change  f  and  i  to ths.) 

2.  Add  -J-  and  |-.  (Change  ^  and  -|  to ths.) 

3.  From  4  subtract  4--  (Change  f  and  i  to ths.) 

4.  From  -f  subtract  4--  (Change  -f  and  i  to ths.) 

5.  Multiply  I  by  3.  (Three  times  .) 

6.  Multiply  I  by  5.  (Five  times  -.) 

■  7.   Multiply  12  by  I .  (Two  thirds  of  .) 

8.  Multiply  15  by  |.  (Two  fifths  of  .) 

9.  Multiply  6  by  2|.  (Two  times  6,  plus  J  of  6.) 

10.  Multiply  41  by  2|.  (Two  times  4^,  plus  J  of  4J.) 

11.  Divide  4  by  f.  (Change  4  to  .) 

12.  Divide  5|-  by  |.  (Change  5^  to  .) 

13.  Divide  ^^J  h  (Change  i  and  i  to  .) 


14.  Divide  |-  by  2.  (One  half  of  .) 

15.  Divide  |  by  3.  (One  third  of  .) 

16.  Find  tlie  sum  of  ^  and  |.  |  -[-  ^  +  4  = 

17.  Find  the  difference  of  |  and  |.  4|  —  1|  = 

18.  Find  the  product  of  |  and  4.       |  x  6  = 

19.  Find  the  product  of  6  and  1|.     8  x  2^  = 

20.  Find  the  quotient  of  5  divided  by  ^. 

21.  Find  the  quotient  of  ^  divided  by  5. 

(a)  From  2154  subtract  10T2f . 

(b)  From  3275  subtract  843f . 

(c)  From  4526  subtract  1283.4. 


188 


ELEMENTARY    ARITHMETIC. 
MEASUREMENTS.* 


2  in. 


1.  The  area  of  a  rectangle  1  inch  wide  and  6 
—  square  inches.     The  area  of  a 


in.  long  is  — 

rectangle  ^  of  an  inch  wide  and  6  in.  long  is  

square  inches. 

2.  The  area  of  a  rectangle  1  inch  wide  and  8 

in.  long  is  square  inches.     The  area  of  a 

rectangle  J  of  an  inch  wide  and  8  in.  long  is  

square  inches. 

3.  The  area  of  a  rectangle  1  in.  wide  and  5  in. 
long  is  square  inches.  The  area  of  a  rect- 
angle i  of  an  inch  wide  and  5  in.  long  is  

square  inches- 

4.  The  area  of  an  oblong  4  inches  wide  and  6 

in.  long  is  square  inches.     The  area  of  an 

oblong  4   inches  wide    and    6^    in.   long  is  

square  inches. 

(a)  Multiply  60  minutes  by  24. 

(b)  Multiply  24  hours  by  31. 

(c)  Multiply  144  square  inches  by  8. 

*  To  THE  Teacher. — Be  sure  that  the  pupil  understands  that 
by  the  expression  square  inch,  we  mean  the  equivalent  of  a  1-inch 
square.  Then  by  paper  cutting  lead  him  to  discover  that  the 
area  of  a  piece  of  paper  |  in.  by  2  in.  is  1  square  inch;  that 
the  area  of  a  piece  of  paper  \  in.  by  4  in,  is  1  square  inch,  etc. 
Remind  the  pujjil  that  a  rectangle  may  be  either  a  square  or  an 
oblong. 


PART   III.  189 


MEASUREMENTS. 


1.  The  area  of  an  oblong  1  ft.  wide  and  6  ft. 

long  is  square  feet.     The  area  of  an  oblong 

J  of  a  foot  wide  and  6  ft.  long  is  square  feet. 

2.  The  area  of  an  oblong  1  ft.  wide  and  8  ft. 

long  is  square  feet.    The  area  of  an  oblong  ^ 

of  a  foot  wide  and  8  ft.  long  is  scjuare  feet. 

3.  The  area  of  an  oblong  1  ft.  wide  and  5  feet 

long  is  square  feet.     The  area  of  an  oblong  | 

of  a  foot  wide  and  5  feet  long  is  square  feet. 

4.  The  area  of  an  oblong  4  feet  wide  and  8  feet 

long  is  square  feet.     The  area  of  an  oblong 

4  ft.  wide   and    8 J  ft.  long  is square  feet. 

The  area  of  an  oblong  4^  ft.  wide  and  8  ft.  long  is 
square  feet. 

5.  A  ^-foot  square  is of  a  square 

foot. 

6.  Draw  upon  the  blackboard  very  carefully  a 
2|-foot  square.  Try  to  divide  it  so  that  you  can 
see  how  many  square  feet  it  contains. 

7.  Draw  upon  the  blackboard  very  carefully  a 
l^-foot  square.  Try  to  divide  it  so  that  you  can 
see  how  many  square  feet  it  contains. 

8.  In  a  3J-foot  square  there  are  square 

feet. 

(a)  Divide  $176  by  $8.        (b)  $177  - 
(c)  Divide  $264  by  $8.        (d)  $267 
(e)  Divide  $336  by  $8.        (f)  $341 


190  ELEMENTARY    ARITHMETIC, 

RATIO    AND    PROPORTION. 


lO*? 


15  cents. 


1.  If  4  lemons  are  worth  10^,  6  lemons  are 
worth  cents. 

4  is — -  of  6.         6  is — -  of  4. 

10  is —of  15.     15  is of  10. 

8  is of  12.     12  is of  8. 

12  is of  18.     18  is of  12. 


2. 


3. 


4.  20^  pays  for  6  lemons;  30^  pays  for  - 

5.  10^  pays  for  4  oranges;  15^  pays  for 

6.  $4  pays  for  12  yards;  $6  pays  for  — 

7.  75^  pays  for  9  yards;  25^  pays  for  — 

8.  15^  pays  for  6  bananas;  10^  pays  for 

9.  $40  pays  for  12  tons;  $10  pays  for  - 


10.  $30  pays  for  9  tickets;  $20  pays  for . 

11.  Susan  has  10^;  Jane  has  15^;  if  Susan  can 
buy  4  pencils,  Jane  can  buy  pencils. 

12.  Henry  has  20^;  William  has  30^;  if  Henry 
can  buy  8  tablets,  William  can  buy  tablets. 

13.  If  4  horses  consume  10  pecks  of  oats  in  a 
day,  6  horses  will  consume  pecks. 

(a)  Divide  $176  by  8.  (b)  $178  -  8  = 

(c)  Divide  $264  by  8.  (d)  $269  -  8  = 

(e)  Divide  $336  by  8.  (f )  $343  -  8  = 


PART  III.  191 

RATIO    AND    PROPORTIOX. 

1.  Twelve   oranges    are  worth  times  as 

much  as  8  oranges.     If  8  oranges  are  Avorth  14^, 
12  oranges  are  worth  cents. 

2.  Fifteen  dozen  eggs  are  worth  times  as 

much  as   10   dozen  eggs.     If  10   dozen  eggs  are 
worth  $1.20,  15  dozen  are  worth  . 


3.  Eight  ponies  consume as  many 

oats  in  a  day  as  12  ponies.     If  12  ponies  consume 
60  qt.,  8  ponies  consume  quarts. 

4.  A  man  can  earn times  as  much  money 

in  6  days  as  he  can  earn  in  2  days.     If  he  earns 
$5  in  2  days,  in  6  days  he  earns  dollars. 

5.  If  10  lbs.  of  sugar  are  worth  40^,  15  lbs. 
are  worth  cents. 

6 .  If  4  acres  of  land  yield  6  tons  of  hay,  at  the 
same  rate  6  acres  yield  tons. 

7.  If  10  railroad  tickets  cost  $4,  at  the  same 
rate  15  tickets  cost  dollars. 

8.  If  4  bushels  of  beans  are  worth  $7,  6  bush- 
els are  Avorth  . 

9.  If  6  bags  of  corn  are  worth  $5,  9  bags  of 
corn  are  worth  . 

10.  If  8  yards  of  velvet  are  worth  $11, 12  yards 
are  worth  . 

(a)  Add  326|,  243,  and  155i. 

(b)  Add  276.2,  144.3,  and  354.6. 

(c)  Add  275,  436,  273,  244. 


192  ELEMENTARY    ARITHMETIC. 

MISCELLANEOUS    PROBLEMS. 

(a)  At  $240  an  acre,  liow  much  will  3.2  acres 
of  land  cost  ? 

(b)  Find  the  cost  of  9  sheep  at  $3.45  a  head. 

(c)  A  lady  paid  $6.80  for  a  hat  and  |  as  much 
for  shoes.     Find  the  cost  of  both. 

(d)  If  7  tons  of  coal  cost  $45.50,  how  much 
does  one  ton  cost  ? 

(e)  A  man  bought  two  horses  for  $300;  he  sold 
one  of  them  for  $160,  and  the  other  for  $180. 
How  much  did  he  gain  ? 

(f)  When  cheese  is  worth  $.08  a  pound,  how 
many  pounds  can  be  bought  for  $28.64. 

(g)  At  $.05  a  pound,  how  many  pounds  of  sugar 
will  cost  $24.50  ? 

(h)  The  lot  upon  which  Mr.  Smitli's  new  house 
stands  cost  $1300;  the  house  cost  6  times  as  much 
as  the  lot.     Find  the  cost  of  both. 

(i)  Mr.  Brown  put  into  the  bank  on  Monday, 
$24.30;  on  Tuesday,  $11.50;  on  Wednesday, 
$13.45;  on  Thursday,  $6.83;  on  Friday,  $42;  on 
Saturday,  $13.75.     How  much  in  all? 

(j)  Mr.  Jones  had  $75.40  in  the  bank;  he  put 
in  $15.20  and  soon  after  drew  out  $42.30.  How 
much  did  he  then  have  in  the  bank  ? 

(a)  From  3246  subtract  1518. 

(b)  From  4624  subtract  2481|. 

(c)  From  2751  subtract  1480.4 


PART   IV. 


DECIMALS HUNDREDTHS. 


1.  24^  and  8^  are  cents. 

2.  .24  and  .08  are  lumdredtlis. 

3.  24^  less  8^  are  cents. 

4.  .24  less  .08  are  hundredths. 

5.  24^  X  2,  means,  2  times  2Jf<^;  2  thnes  24^  = 

6.  .24  X  2,  means,  f  times  .2Jf  ',  2  times  .24  = 

7.  24^  -f-  4^,  means,  find  how  many  times  Jf<^ 
are  contained  in  2Jf(^;  4:^  are  contained  in  24^ 
times. 

8.  .24  -^  .04,  means,  find  Jioiv  many  times  .OJj. 

are  contained  in  .2Jf',   -04  are  contained  in  .24 

times. 

9.  24^  ^  4,  means,  ^;2<:?  one  fourth  of  24^  ;  one 
fourth  of  24^  is  cents. 

10.  .24  -^  4,  means,  y^nc^  one  fourth  of  .2Jfj  one 
fourth  of  .24  is  hundredths. 

(a)  Multiply  $224  by  2.  (b)  $2.24  x  2  = 
(c)  Multiply  $235  by  2.  (d)  $2.35  x  2  = 
(e)  Multiply  $346  by  2.      (f)  $3.46  x  2  := 

193 


194                       ELEMENTARY    ARITHMETIC. 
DECIMALS HUNDREDTHS. 

1.  One  himdredtli  of  a  dollar  is  cent. 

2.  Six  hundredths  of  a  dollar  =  cents. 

3.  53  hundredths  of  a  dollar  =  cents. 

4.  46  hundredths  =  tenths  and  . 

5.  52  hundredths  =  tenths  and  . 

6.  $.45  =   tenths  and  hundredths 

of  a  dollar. 

7.  $.36  =  tenths  and  hundredths 

of  a  dollar. 

8.  One    half-dollar  =    hundredths    of   a 

dollar. 

9.  One  fourth-dollar  =  hundredths  of  a 

dollar. 

10.  Mary  had  $.08  in  her  pocket  and   $.52  in 
her  bank ;  in  both  she  had  . 

11.  Jane  had  $.48;   she  spent  $.11;    she  then 
had  . 

12.  Sarah  i^aid  $.25  for  each  of  3  books;  for  all 
she  paid  . 

13.  Alice  had  $.50  with  which  to  buy  tea  at 
$.25  a  pound;  she  could  by  . 

14.  Maude  paid   $.80   for  4  pounds  of  coffee; 
one  pound  cost  . 


(a)  Divide  $198  by  $9.     (b)  $199 


(c)  Divide  $297  by  $9.     (d)  $299  -  $9  = 


(e)  Divide  $306  by  $9.     (f )  $309 


$9 


$9  = 


PART  IV.  ,  195 

DECIMALS HUNDREDTHS. 

1.  .28  +  .06.       (To  be  read,  28  liimdredtlis  plus    6 
hundredths.) 

.28  +  .06,  means,  .28  and  .06  ;  .28  and  .06  = 
Arthur  earned  .28  of  a  dollar  Monday  and  .06 
of  a  dollar  Tuesday ;  in  both  days  he  earned . 

2.  .32  —  .06.     (To  be  read,  32  hundredths  minus  6 
hundredths.) 

.32  -  .06,  means,  .32  less  .06 ;  .32  less  .06  = 
Harry  had  .32  of  a  dollar;   he  spent  .06  of  a 
dollar;  he  then  had  . 

3.  .06x4,    (To  be  read,  6  hundredths  multiplied  by  4.) 
.06  X  4,  means,  ^  times  .06;  4  thnes  .06  are 

If  1  yard  of  ribbon  is  wortli  .06  of  a 


dollar,  4  yards  are  worth 

4.  .48  -^  .06.  (To  be  read,  48  hundredths  divided  by 
6  hundredths.) 

.48  ^  .06,  means,  find  how  many  times  .06  are 
contained  in  .4-8;   .06  are  contained  in  .48  . 

James  had  .48  of  a  dollar  with  which  to  buy 
tablets  at  .06  of  a  dollar  each;  he  could  buy . 

5.  .48  ^  6.     (To  be  read,  48  hundredths  divided  by  6.) 
.48  -^  6,  means,  find  1  sixth  of  .Jf8;  1  sixth  of 

.48  is  .     William  paid  .48  of  a  dollar  for 

6  pounds  of  sugar;  one  pound  cost  . 

(a)  Divide  $198  by  9.     (b)  $1.98  by  9  = 
(c)  Divide  $297  by  9.     (d)  $2.97  by  9  = 


196                       ELEMENTARY    ARITHMETIC. 
DECIMALS HUNDREDTHS. 

1.  The  sum  of  $.2  and  $.34  is  — 

2.  The  sum  of  $.43  and  $.04  is  - 

3.  The  sum  of  $.30  and  $.06  is  - 

4.  The  sum  of  $.40  and  $.05  is  - 


5.  The  sum  of  $.08  and  $.96  is  - 

6.  The  sum  of  $.25  and  $.06  is  - 

7.  The  sum  of  $.09  and  $.06  is  - 

8.  The  sum  of  $.35  and  $.07  is  - 

9.  The  sum  of  $1.25  and  $1.25  is 

10.  The  sum  of  $1.35  and  $.08  is  - 

11.  The  sum  of  $1.45  and  $.4  is  - 

12.  The  sum  of  $1.55  and  $.6  is  - 


13.  The   sum  of    two    tenths    and   twenty-four 
hundredths  is hundredths. 

(a)  $26.2  +  $84.24  = 

14.  The  sum  of  eight  tenths  and  six  hundredths 
is  hundredths,     (b)  $47.8  f  $55.06  = 

15.  The  sum  of  seven  hundredths  and  ^xe  hun- 
dredths is  hundredths. 

(c)  $36.07 +  $45.05  = 

16.  The  sum  of  fifty  hundredths  and  fifty-five 
hundredths  is  hundredths. 

(d)  $64.50  +  $73.55  = 

(e)  Add  26.24,  15.2,  and  43.36. 

(f)  Add  35.2,  47.34,  and  48.24. 

(g)  Add  84.25,  6.34,  2.58,  and  31.21. 


PART  IV.  197 


DECIMALS HUNDREDTHS. 


1.  The  difference  of  $.45  and  $.25  is 

2.  The  difference  of  $.6  and  $.15  is  - 

3.  The  difference  of  $.40  and  $.05  is 

4.  The  difference  of  $.45  and  $.2  is  - 


5. 

$2.30  -  $1.25  = 

2.30  -  1.28 

6. 

$3.45  -  $1.05  - 

3.45  -  1.03 

7. 

$4.55-  $2.2  = 

4.55  -  2.3  : 

8. 

$5  -  $.25  = 

5  -  .75  = 

(a)  From  20  dollars  and  45  cents  subtract  14 
dollars  and  22  cents. 

(b)  From  26   and  45   hundredths  subtract   14 
and  24  hundredths. 

(c)  Add  35  dollars  and  45  cents,  and  27  dollars 
and  53  cents. 

(d)  Add  35  and  24  hundredths,  and  27  and  42 
hundredths. 

(e)  From  38  dollars  and  52  cents  subtract  21 
dollars  and  27  cents. 

(f)  From   38   and    52   hundredths   subtract   21 
and  24  hundredths. 

(g)  Add  twenty-four  dollars  and  forty-two  cents 
and  thirty-three  dollars  and  twenty-seven  cents. 

(h)  From  37.24  subtract  12.18 
(i)  From  86.37  subtract  28.3. 
(j)  From  97.8  subtract  34.25. 


198                       ELEMENTARY    ARITHMETIC. 
DECIMALS HUNDREDTHS. 

1.  The  product  of  $.12  multiplied  by  2  - 

2.  The  product  of  $1.04  multiplied  by  5 

3.  The  product  of  $2.25  multiplied  by  3 

4.  The  product  of  $1.50  multiplied  by  2 

5.  $2.25  X  2=  1.25  X  3  = 

6.  $2.12  X  3=  2.12  X  4  = 

7.  $3.04  X  4=  3.04  x  5  = 

8.  $4.25  X  4=  4.25  x  5  = 


(a)  Multiply  15  dollars  and  26  cents  by  5. 

(b)  Multiply  15  and  27  hundredths  by  5. 

(c)  Multiply  24  dollars  and  35  cents  by  6. 

(d)  Multiply  24  and  32  hundredths  by  6. 

(e)  Multij^ly  34  dollars  and  3  dimes  by  4. 

(f)  Multiply  34  and  4  tenths  by  4. 

(g)  Multiply  twenty-eight  dollars  and  sixteen 
cents  by  three. 

(h)  Multiply  twenty-eight  and  sixteen  hun- 
dredths by  four. 

(i)  Multiply  forty-three  dollars  and  twenty-five 
cents  by  four. 

(j)  Multiply  forty -three  and  twenty-five  hun- 
dredths by  three. 

(k)  Multiply  forty-six  and  three  tenths  by  seven. 

(1)  Multiply  $245  by  5.  (m)  $2.45  x  5  =-- 
(n)  Multiply  $375  by  5.  (o)  $3.75  x  5  = 
(p)  Multiply  $237  by  5.        (q)  $2.37  x  5  - 


PART   IV. 


199 


DECIMALS HUXDREDTHS. 


1.  The   quotient  of    $.45   divided  by   $.05   is 


3.  The  quotient  of  .55  divided 

by  .05  is  

4.  The  quotient  of  ,55  divided  by  5  is  . 

5.   $.36  -  $.09  =                .36  -  .04  = 

6.  $.36- 

-  9  =                      .36  - 

-4  = 

7.   $.48- 

-  $.06  =                .48  - 

-.04  = 

8.  $.48- 

-  6  =                     .48  - 

-4  = 

9.  $.12- 

-$.02=                .12- 

-.03  = 

10.  $.12- 

-2=                     .12- 

-3  = 

11.  $1.20-  $.02  =            1.20- 

-.03  = 

12.  $1.20-2=                  1.20- 

-3  = 

(a)  Divide  24  dollars  and  25  cents  by  5^. 

(b)  Divide  24  and  25  hundredths  by  .05. 

(c)  Divide  37  dollars  and  5  cents  by  5  cents. 

(d)  Divide  37  and  5  hundredths  by  5  hundredths 

(e)  Divide  37  dollars  and  5  cents  by  5. 

(f )  Divide  37  and  5  hundredths  by  5. 

(g)  Divide  $2.25  by  $.05. 

(h)  $6.75  -  $.05  = 

(i)  Divide  $3.45  by  $.05. 

(j)  $4.35-  $.05=     , 

(k)  Divide  $7.15  by  $.05. 

(1)  $8.55 

-  $.05  = 

200                       ELEMENTARY    ARITHMETIC. 
DECIMALS HUNDREDTHS. 

1.  One  half  of  .24  is  .       .24  is  |  of 

2.  One  half  of  .16  is  .       ,16  is  ^  of 

3.  One  third  of  .12  is  ■ -.  .    .12  is  4  of 

4.  Two  thirds  of  .12  are  . 


.12  is  I  of 


5.  Three  fourths  of  .12  are 

6.  One  half  of  2.06  is  


.12  is  I  of 


2.06  is  4-  of  . 

7.  .08  is  what  part  of  .12?  .04  of  .12? 

'       8.  .09  is  what  part  of  .12?  .06  of  .12? 

9.  .12  is  what  part  of  .16?  .12  of  .18? 

10.  .12  is  what  part  of  .36?  .12  of  .48? 

11.  .25  is  what  part  of  1?  .75  of  1? 

12.  One  fourth  of  .2  (.20)  is  hundredths. 

13.  Three    fourths    of    .2   (.20)   are  hun- 
dredths. 

14.  One  fifth  of  .2  (.20)  is  hundredths. 

15.  Three  fifths  of  .2  (.20)  are hundredths. 

16.  .04  is of  .2.      .05  is of  .2. 

17.  .08  is of  .2.      .12  is ^  of  .2. 

18.  .15  is ^  of  .2.      .16  is of  .2. 


(a)  Divide  $24.48  by  6.  (b)  $2449 

(c)  Divide  $35.04  by  6.  (d)  $3505 

(e)  Divide  $29.47  by  7.  (f)  $2949 

(g)  Divide  $43.25  by  5.  (h)  $4326 


PART   ]V.  201 

DECIMALS HUNDREDTHS. 

1.  One  hundredth  of  200  is . 

.02  of  200  = 


02  of  300 


2.  One  hundredth  of  300  is  

3.  One  hundredth  of  400  is  

4.  Three  hundredths  of  200  are  . 

.04  of  200  = 

5.  Three  hundredths  of  300  are  . 


02  of  400  = 


.04  of  300  = 

6. 

.01  of  202  = 

.02  of  202  = 

.03  of  202 

7. 

.01  of  302  = 

.02  of  302  = 

.03  of  302 

8. 

.01  of  108  = 

.02  of  108  = 

.03  of  108 

9. 

.01  of  212  = 

.02  of  212  = 

.03  of  212 

10. 

.01  of  240  = 

(a)  Find 

.02  of  240. 

11. 

.01  of  243  = 

(b)  Find 

.02  of  243. 

12. 

.01  of  320  = 

(c)  Find 

.03  of  320. 

13. 

.01  of  324  = 

(d)  Find 

.03  of  324. 

14. 

.01  of  230  = 

(e)  Find 

.05  of  230. 

15. 

.01  of  236  :.= 

(f)  Find 

.07  of  236. 

16. 

.01  of  26  = 

(g)  Find 

.08  of  26. 

17. 

.01  of  45  = 

(h)  Find 

.05  of  45. 

18. 

.01  of  535  = 

(i)  Find 

.03  of  535. 

(j)  Add  3.05,  2.75,  25.3,  and  346. 
(k)  Add  45.03,  6.4,  325.2,  and  240. 
(1)  Add  6.21,  64.5,  146.2,  and  150. 


202                       ELEMENTARY    ARITHMETIC. 
DECIMALS HUNDREDTHS. 

1.  One  hundredth  of  6  is  hundredths. 

2.  One  hundredth  of  3  is  hundredths. 

3.  One  hundredth  of  5  is  hundredths. 


4.  One  hundredth  of  $8  is  .     .04  of 

5.  One  hundredth  of  $6  is  .     .07  of  $6 

6.  One  hundredth  of  $9  is  .     .06  of  $9 


.03  of  $25  = 


.02  of 


7.  One  hundredth  of  $25  is  - 

8.  One  hundredth  of  $32  is  - 

9.  One  hundredth  of  $43  is  . 

.02  of  $43  = 

10.  One  tenth  of  $3  is  .  .2  of  $3  = 

11.  One  hundredth  of  $3  is  . 

.02  of  $3  = 

12.  One  tenth  of  $5  is  .  .3  of  $5  = 

13.  One  hundredth  of  $5  is  . 

.03  of  $5  = 

14.  One  tenth  of  $12  is  .        .02  of  $12  = 

15.  One  hundredth  of  $12  is  . 

.02  of  $12  = 

16.  One  tenth  of  $120  is  .       .2  of  $120  = 

17.  One  hundredth  of  $120  is  . 

02  of  $120  = 

(a)  From  24.4  subtract  12.27. 

(b)  From  325.2  subtract  43.35. 

(c)  From  146.25  subtract  84.82. 


PART    IV.  203 

DECIMALS HUXDREDTHS. 

1.  Harry  paid  $2  for  100  pencils;  one  pencil 
cost  liundreclths  of  a  dollar. 

2.  Arthur  paid  $4  for  10  First  Readers;  one 
First  Reader  cost  tenths  of  a  dollar. 

3.  Mr.  Jones  paid  $26  for  100  watermelons; 
one  watermelon  cost  . 

4.  Mr.  Rice  paid   $45  for  10  cords  of  wood; 
one  cord  of  wood  cost  . 

5.  If  one  pound  of  sugar  is  worth  $.04,  100 
pounds  of  sugar  are  worth  . 

6.  If  one  ton  of  coal  is  worth  $6.50,  10  tons 
of  coal  are  worth  . 

7.  One  bushel  of  wheat  weighs  60  pounds;  10 
bushels  of  wheat  weigh  . 

8.  One  bushel  of  oats  weighs  32  pounds;  100 
bushels  of  oats  weigh  . 

(a)  Find  7  hundredths  (.07)  of  324. 

Operation.  Explanation. 

3 ''24  .01  of  324  =  3.24 

.07  .07  of  324  =  22.68 

22.68 

(b)  Find  .06  of  437.  (c)  .5  of  437  := 

(d)  Find  .04  of  356.  (e)  .4  of  248  =. 

(f)  Multiply  $342  by  5.  (g)  $3.42  x  5. 
(h)  Multidly  $235  by  4.  (i)  $2.35  x  4. 
(j)  Multiply  $148  by  6.      (k)  $1.48  x  6. 


204 


ELEMENTARY    ARITHMETIC. 


DECIMALS HUNDREDTHS. 


1.  600  X  .03,  means 

2.  400  X  .03,  means 

3.  200  X  .08,  means 

4.  500  X  .07,  means 

5.  123  X  .01,  means 

6.  123  X  .02,  means 

7.  241  X  .02,  means 

8.  222  X  .03,  means 

9.  $24  X  .01,  means 

10.  $24  X  .02,  means 

11.  $32  X  .03,  means 

12.  $62  X  .03,  means 

13.  $6  X  .01,  means  - 

14.  $6  X  .02,  means  - 

15.  $8  X  .09,  means  - 

16.  $7  X  .05,  means  - 


12    X  3  = 


23  X  3 


17. 
18. 

19.  $62  X  2 

20.  $26  X  2 


$2  X 
$23  X 
$62  X 
$26  X 


.03  of  600  = 
.03  of  400  = 
.08  of  200  = 
.07  of  500  = 

.01  of  123  = 
.02  of  123  =. 
.02  of  241  = 

.03  of  222  = 

.01  of  $24  = 
.02  of  $24  = 
.03  of  $32  =:= 
.03  of  $62  = 

.01  of  $6  = 
.02  of  $6  = 
.09  of 
.05  of 


$2  X  .03  = 
$23  X  .03  = 
$62  X  .02  = 
$26  X  .02  = 


(a)  Divide  $4.36  by  $.04.  (b)  5.24 

(c)  Divide  $6.24  by  $.04.  (d)  7.24 

(e)  Divide  $5.44  by  $.04.  (f)  5.68 

*600  X  .03,  means,  find  .03  of  600. 


.04 

.04 
.04 


PART  IV.  205 


DECIMALS HUNDREDTHS. 


1.  When  coal  costs  $4  per  ton, — 

2  tons  cost  .  3  tons  cost  

.1  of  a  ton  costs  .       .2  of  a  ton  cost 

.3  of  a  ton  cost  .       2.1  tons  cost  — 

2.2  tons  cost  .  2.3  tons  cost  — 


2.  When  land  costs  $300  per  acre, — 
2  acres  cost  .  3  acres  cost  — 


.1  of  an  acre  costs .      .2  of  an  acre  cost 

.3  of  an  acre  cost .      .4  of  an  acre  cost 

.01  of  an  acre  costs .    .02  of  an  acre  cost 

.03  of  an  acre  cost .    .04  of  an  acre  cost 

2.1  acres  cost  .  2.2  acres  cost  

2.01  acres  cost  .         2.02  acres  cost  


3.  When  coal  costs  $6  per  ton, — 

2  tons  cost  .  3  tons  cost  

.1  of  a  ton  costs  .       .2  of  a  ton  cost 

1.1  tons  cost  .  2.1  tons  cost  — 


4.  When  corn  meal  costs  $20  per  ton, — 

2  tons  cost  .  3  tons  cost  . 

.1  of  a  ton  costs  .       .2  of  a  ton  cost  - 

.01  of  a  ton  costs .      .02  of  a  ton  cost 

.3  of  a  ton  cost  .         .03  of  a  ton  cost 

2.1  tons  cost  .  1.01  tons  cost  


(a)  Divide  $4.36  by  4.     (b)  5.25  -  4  = 
(c)  Divide  $6.24  by  4.     (d)  7.33  -  4  = 


206                       ELEMENTARY    ARITHMETIC o 
DECIMALS HUXDREDTIIS. 

(a)  Multiply  $234  by  3.25.  This  means,  find 
three  times  $^SJf  iilus  two  tenths  of  $2SJf  i^ls 
five  hundredths  of  $2oJf. 

Operation  No.  1.  Explanation. 

1234.  Three  times  $234  are  $702.  ' 

o*25  One  tentli  of  $234  is  $23.4. 

^       Two  tenths  of  $234  are  $46.8. 

$702.       (3  times  $234.)  One  hundredth  of  $234  is  $2.34. 

$46.8     (.2  of  $234.)  Five  hundredths  of  $234  are 
$11.70  (.05  of  $234.)  $11.T0. 

$760:50  (3.25  times  ^234.)*^^^+^^^-^+^^^-^^=^^^^-^^ 

Operation  No.  2.  •  Explanation. 

^234  One  hundredth  of  $234  is  $2.34. 

Q  or  Five  hundredths  of  $234  are 

. ^:^  $11.70. 

$11.70  (.05  of  $234.)        One  tenth  of  $234  is  $23.4. 
$46.8    (.2  of  $234.)  Two  tenths  of  $234  are  $46.8. 

$702.       (3  times  $234.)      Three  times  $234  are  $702. 

$760:50  (3.25  times  |234.)^^^-^^+^^^-^+^^^^=^^^^-^^ 

SUGGESTED    NUMBER    STORY. 

If  one  acre  of  land  is  worth  $324, 

1  hundredtli  of  an  acre  is  worth  . 


5  hundredths  of  an  acre  are  worth 

1  tenth  of  an  acre  is  worth  . 

2  tenths  of  an  acre  are  worth  

3  acres  are  worth  . 


3.25  acres  are  worth  -. 

(b)  Add  3.25,  24.6,  48,  375,  and  42. 


PART    lY.  207 

DECIMALS HUNDREDTHS. 

1.  A  farmer  paid  $4.2  for  a  sheep  and  $2.25 
for  a  lamb ;  for  both  he  paid  . 

(a)  A  farmer  j)aid  $125  for  a  horse,  $95  for  a 
buggy,  and  $24.50  for  a  harness.  How  much  did 
he  pay  for  all  ? 

2.  A  boy  paid  $4.65  for  a  coat  and  a  pair  of 
shoes;  for  the  shoes  he  paid  $2.2 ;  for  the  coat  he 
paid  . 

(b)  A  man  paid  $346.5  for  wood  and  coal ;  for 
the  wood  he  paid  $38.25.    How  much  for  the  coal  ? 

3.  Harry  had  $5  ;  he  spent  $2  for  books  and 
$2.55  for  clothing;  he  then  had  . 

(c)  Harry's  father  had  $645.75;  he  spent  $25.2 
for  groceries  and  $34.75  for  fuel.  How  much 
money  had  he  left  ? 

4.  If  one  load  of  wood  is  worth  $4.25,  two 
loads  are  worth  . 

(d)  At  $275.25  an  acre,  how  much  are  four 
acres  of  land  worth  ? 

5.  William  paid  $.4  for  oranges  at  $.05  each; 
he  bought  oranges. 

(e)  William's  father  paid  $19.6  for  posts  at  $.08 
each.     How  many  posts  did  he  buy  ? 

(f)  From  375.25  subtract  148.17. 

(g)  From  464.2  subtract  238.46. 
(h)  From  645.34  subtract  582.8. 


208                       ELEMENTARY    ARITHMETIC. 
DECIMALS HUNDREDTHS. 

1.  At  $300  a  mile,  how  much  will  it  cost  to 

make  2.25  miles  of  road?     2  miles  cost  ;  2 

tenths  of  a  mile  cost  ;  5  hundredths  of  a  mile 

cost  ;  2.25  miles  cost  . 

(a)  At  $345  a  mile,  how  much  will  it  cost  to 
make  3.25  miles  of  road?  $345  x  3.25  = 
$345  X  3i  = 

2.  Alice  paid  $1.26  for  some  tablets  that  cost 
$.06  each;  there  were  tablets. 

$.05)$. 60      $.05)$.65       $.05)$2      $.05)$2.25 

(b)  Mr.  Dunn  paid  $25.02  for  paper  that  cost 
$.06  a  pound.     How  many  pounds  were  there? 

3.  Sarah  paid  $1.60  for  4  yards  of  ribbon;  one 
yard  cost  . 

4)$1.20  4)$1.4  8)$1.6  8)$1.2 

(c)  Mr.  King  paid   $52.6t)  for  4  tons  of  bran. 
How  much  did  it  cost  per  ton? 

4.  Charlie  paid  $.12  for  3  pencils;  at  the  same 
rate  7  pencils  would  cost  — — . 

(d)  Mr.  Johnson  paid  $26.50  for  2  tons  of  hay. 
At  the  same  rate  how  much  would  7  tons  cost? 

(e)  Multiply  $521  by  4.25.     (f )  $346  x  2.25  = 
(g)  Multiply  $435  by  6.25.     (h)  $164  x  5.25  = 


PART  IV.  209 

DECIMALS HUNDREDTHS. 

1.  Mr.  Bliss  had  .72  of  an  acre  of  land  which 
he  divided  into  lots  each  containing  .09  of  an  acre; 
there  were  lots. 

.09  of  an  acre)1.80  acres.     .09  of  anacre)2.79  acres. 

(a)  Mr.  Wheeler  had  3.78  acres  of  land  which 
he  divided  into  lots  each  containing  .09  of  an 
acre.     How  many  lots  ? 

2.  Dr.  Harris  had  6.36  acres  of  land ;  he  divided 
it  into  3  equal  lots  ;  each  lot  contained . 

2)4.18  acres.  2)6.06  acres. 

(b)  Gen.  Dow  had  76.25  acres  of  land  which  he 
divided  into  5  equal  lots.     How  much  in  each  lot? 

3.  Mr.  Parker  had  4  equal  lots  of  land;  each 
lot  contained  1.05  acres;  in  all  he  had  . 

3.06  acres.      2.08  acres.      2.22  acres.      7.33  acres. 
4  5  3  2 


(c)  Mr.  Green  had  4  equal  lots  of  land;  each 
lot  contained  35.24  acres.  How  much  land  had 
he  in  all? 

(d)  Divide  2.48  by  .04. 
(f)  Divide  6.72  by  .06. 
(h)  Divide  8.54  by  .07. 


(e)  3.65  - 

.05 

(g)  7.32  -. 

.06 

(i)    1.20  - 

.08 

210  ELEMENTARY    ARITHMETIC. 

DECIMALS HUNDREDTHS. 

1.  Robert  had    $1.25;    tliis  is  4    as   much  as 
Peter  had;  Peter  had — . 

(a)  Mr.  Hill  had  $24.45;  this  is  |  as  much  as 
Mr.  Ford  had.  How  much  money  did  Mr.  Ford 
have  ? 

2.  Frank's  book  cost  $1.20;  his  slate  cost  |  as 
much  ;  his  slate  cost  . 

(b)  Mrs.  Ford's  carpet  cost  $54.78;  her  cur- 
tains cost  I  as  much.  How  much  did  her  curtains 
cost  ?  ^ 

3.  When  apples  are  worth  $.40  a  bushel,  ^  of 

a  bushel  is  worth  .     f  of  a  bushel  are 

worth  . 

(c)  When  meal  is  worth  $18  per  ton,  how  much 
is  i  of  a  ton  worth  ?     f  of  a  ton  ? 

4.  James  paid  $.60  for  f  of  a  bushel  of  peaches  ; 
at  the  same  rate,  a  bushel  would  cost  — . 

(d)  Mr.  Keen  paid  $6.45  for  |  of  a  ton  of  coal. 
At  the  same  rate  how  much  would  :^  of  a  ton  cost  ? 
How  much  would  1  ton  cost  ? 

5.  If  2  yards  of  muslin  are  worth  $.12,  seven 
yards  are  worth . 

(e)  If  two  barrels  of  apples  are  worth  $6.50, 
how  much  are  five  barrels  worth  ?     Seven  barrels  ? 

(f)  Divide  3.56  by  4.  (g)  2.75 
(h)  Divide  6.42  by  6.             (i)  7.44 


(j)  Divide  9.24  by  7.  (k)  1.36  -  8  = 


PART   lY. 

DECIMALS— 

-HUNDREDTHS. 

1. 

$300  X  .2  = 

(a)   $370  X  .2  = 

2. 

$320  X  .2  = 

(b)   $328  X  .2  = 

3. 

$300  X  .02  = 

(c)  $345  X  .02  = 

4. 

$300  X  2.2  = 

(d)  $370  X  2.2  = 

5. 

$300  X  2.02  = 

(e)  $345  X  2.02  = 

6. 

$300  X  2.22  = 

(f )    $234  X  2.22  = 

7. 

$4  -$.2=: 

(g)  $24 -$.2  = 

8. 

$6  -  $.02  = 

(h)  $36  -  $.02  = 

9. 

$3.4-  $.2  = 

(i)    $43.4-  $.2  = 

10. 

$6.4.4-  $.02  = 

(j)   $56.38- $.02 

11. 

$2.4-  $.02  = 

(k)  $34.4  -  $.02  = 

12. 

$4.8-  $1.2  = 

(1)    $52.8-  $1.2  = 

13. 

$2.50-  $1.25  = 

(m)$7.50-  $1.25 

14. 

$3- $1.50  = 

(n)  $27  -  $1.50  = 

15. 

$4.4-2  = 

(o)  $46.8-2  = 

16. 

$1.6-2  = 

(p)  $47.8-2  = 

17. 

$4.04-2  = 

(q)  $74.04-2  = 

18. 

$6.66-2  = 

(r)  $56.38  -  2  = 

19. 

$4.5-5  = 

(s)  $37.5-5  = 

20. 

$.35-5  = 

(t)  $6.35-5  = 

21. 

$5.35  ^  5  = 

(u)  $35.25  -  5  = 

22. 

$8.88-4  = 

(v)  $73.28-4  = 

211 


(w)  Add  374.2,  46,  4.5,  and  243.25. 
(x)  Add  2454,  174|,  and  328|. 
(y)  Add  142^,  234.3,  and  156.2. 


212  ELEMENTARY    ARITHMETIC. 

DECIMALS HUXDREDTHS. 

(a)  Find  the  sum  of  $46,  $275,  and  $342.27. 

(b)  Find  the  difference  of  $467.2  and  $275.38. 

(c)  Find  the  product  of  $345.24  multiplied  by  4. 

(d)  Find  the  product  of  $2746  multiplied  by  .5. 

(e)  Find  the  product  of  $35.62  multiplied  by  .05. 

(f )  Find  the  product  of  $624  multiplied  by  2.5. 

(g)  Find  the  product  of  $734  multiplied  by  3.05. 
(h)  Find  the  product  of  $476  multiplied  by  2.35. 

(i)    Find  the  quotient  of  382.5  divided  by  .5. 
(j)    Find  the  quotient  of  382.5  divided  by  5. 

(k)  Find  the  quotient  of  $28.50  divided  by  $.05. 
(1)    Find  the  quotient  of  $28.50  divided  by  5. 

(m)  Find  the  quotient  of  74.4  divided  by  .4. 
(n)  Find  the  quotient  of  74.4  divided  by  4. 

(o)   Find  the  quotient  of  85.2  divided  by  .6. 
(p)  Find  the  quotient  of  85.2  divided  by  6. 

1.  Find  f  of  $1.2.         (q)  Find  f  of  $37.8. 

2.  $1.2  is  J  of  what?    (r)  $37.8  is  f  of  what? 

3.  Find  I  of  $.18.         (s)  Find  f  of  $4.74. 

4.  $.18  is  I  of  what?    (t)  $4.74  is  f  of  what? 

(u)  From  564.7  subtract  146^. 
(v)  From  352.75  subtract  234^. 
(w)  From  634.32  subtract  247. 16, 


PAKT  IV. 

SIMPLE    NUMBERS. 

(a) 

12  dollars 
3 

36  dollars 

15  oranges 
5 

75  oranges 

213 


(c) 

3 

75^ 

1.  In  problem  (a)    tlie  multiplicand  is  ; 

the  multiplier  is  ;  the  product  is  . 

2.  In  j)roblem  (b)  the  multij)lier  is ;  the 

product  is  ;  the  multiplicand  is  . 

3.  In  problem   (c)   the   product  is  ;  the 

multiplier  is  ;  the  multiplicand  is  . 

4.  In  a  problem  the  product  is  36  dollars;  the 
multiplier  is  4  ;  the  multiplicand  is  . 

5.  The  product  of  two  numbers  is  45 ;  one  of 
the  numbers  is  5 ;  the  other  number  is . 

6.  N.  B. — The  multiplier  can  never  be  a  num- 
ber of  dollars  or  cents  or  oranges  or  books  or  feet 
or  inches.  It  is  always  sbnphj  a  nmnher  that  tells 
how  many  times  the  multiplicand  is  to  be  taken. 

7.  Two  cents  multipUed  hy  tivo  cents  —  nonsense. 

8.  If  the  multiplicand  is  bushels,  the  product 

is  ;  if  the  multiplicand  is  square  inches,  the 

product  is  square  inches. 

(d)  Multiply  144  square  inches  by  9. 

(e)  Multiply  275  bushels  by  23. 

(f)  Multiply  348  dollars  by  2.3. 


214  ELEMENTARY   ARITHMETIC. 

DENOMINATE    NUMBERS. 

16  ounces  =  1  lb. 

1.  Two  poimcls  are  ounces. 

2.  Three  pounds  are  ounces. 

3.  One  half  of  a  pound  is  ounces. 

4.  One  fourth  of  a  pound  is  ounces. 

5.  One  eighth  of  a  pound  is  ounces. 

6.  Three  fourths  of  a  pound  are ounces. 

7.  Three  eighths  of  a  pound  are  ounces. 

8.  One  and  ^  pounds  are  ounces. 

9.  When  cheese  costs  16^   a  pound,  1  ounce 

costs cent;  ^j  lb.  costs  cents;  5  ounces 

cost  ■ cents. 

10.  Henry  bought  1  lb.  7  oz.  of  cheese  at  16^  a 
pound;  the  cheese  cost  cents. 

11.  2  lb.  8  oz.  grapes  at  10^  a  pound  cost . 

12.  lib.  4  oz.  meat  at  12^  a  pound  cost . 

13.  1  lb.  8  oz.  meat  at  12^  a  pound  cost . 

14.  Mary  gave  a  salesman  3  dimes  in  payment 
for  2  lb.  8  oz.  maple  sugar  at  10^  a  pound;  she 
should  receive  in  change  cents. 

15.  Arthur  gave  a  salesman  i  of  a  dollar  in 
payment  for  1  lb.  6  oz.  cheese  at  16^  a  pound;  he 
should  receive  in  change  cents. 

(a)  Divide  34.5  by  .3.  (b)  34.6  -  .3  = 
(c)  Divide  53.2  by  .4.  (d)  53.5  -  .4  =^ 
(e)  Divide  62.5  by  .5.         (f )  62.6  -  .5  - 


PART  IV. 


215 


COMMOX    P^RACTIONS. 

1.  One  half  is  sixteenths. 

2.  One  fourth  is  sixteenths. 

3.  One  eighth  is  sixteenths. 

4.  Three  eighths  are  sixteenths. 

5.  One  fourth  and  1  sixteenth  are  

6.  One  fourth  less  1  sixteenth  are 

7.  Three  eighths  and  1  sixteenth  are  — 

8.  Three  eighths  less  1  sixteenth  are  - 


4-  -^^- 

I      1  6 
3 


g,  means, 


j-g-,  means, 


YT  ^  ^?  means, 

3 


9. 
10. 
11. 

12.  12  X 

13.  12  X  2|,  means 

14.  I  -^  y^y-,  means, 

15.  2^1,  means,  - 
16 


^,  means. 


2,  means, 


+ 


3      _ 

3      _ 

IT  — 


1  6 


o  times  Vtt  = 


^of  12 


2|-  times  12  = 


tV  1^ 


f  are 
iof  - 


17.  A  rectangle  1^-  inches  wide  and  10  inches 
long  contains  square  inches. 

(a)  A  piece  of  land  is  1^^  feet  wide  and  246  feet 
long.     How  many  square  feet  does  it  contain? 

18.  Two  thirds  of  27  are  one  half  of  . 

19.  Three  fourths  of  36  are  one  half  of  . 


(b)  Divide  34.8  by  3. 

(c)  34.5  - 

-  3 

(d)  Divide  53.6  by  4. 

(e)  51.2  - 

-  4 

(f)  Divide  61.5  by  5. 

(g)  63.5  . 

-5 

216  ELEMENTARY    ARITHMETIC. 

COMMON    FRACTIONS. 

1.  Add  I  and  y^.      (Change  |  to  Yg-- 

2.  Add  |-  and  |.        (Change  |  to  -g. 

3.  From  j%-  subtract  |-.     (|  =  y-g.) 

4.  From  |-  subtract  ^.       (|  =  -j.) 

5.  Multiply  10  by  2|.     (2  times  10,  plus  |  of  10.) 

6.  Multiply  6|  by  4.       (4  times  |,  plus  4  times  6.) 

7.  Divide  |  by  2.       (Find  1  half  of  f.) 

8.  Divide  2  by  4-         (Find  how  many  times,  etc.) 

9.  Find  the  sum  of  5-g-  and  5yV- 

10.  Find  the  sum  of  3|-  and  Oy^- 

11.  Find  the  difference  of  8f  and  4:^^. 

12.  Find  the  difference  of  6  and  2y^. 


13.  Find  the  ^^roduct  of  8  multiplied  by  2 


3 


14.  Find  the  product  of  2|  multiplied  by  8. 

15.  Find  the  quotient  of  |-  divided  by  4. 

16.  Find  the  quotient  of  4  divided  by  |. 

17.  A  surface  is  8  inches  long  and   5^  inches 
wide ;  it  contains  square  inches. 

(a)  A  surface  is  46  feet  long  and  6|-  feet  wide. 
How  many  square  feet  is  it  ? 

(b)  Add  256.4,  25.34,  52,  and  1.75. 

(c)  Add  624|,  346,  and  138yV. 

(d)  Add  150],  275,  and  234.25. 


PART  IV.  217 

MISCELLANEOUS    PROBLEMS. 

1.  Thomas  sells  oranges  for  20^  a  dozen;  this 
is  6^  a  dozen  more  than  he  paid  for  them ;  he  paid 
a  dozen. 

(a)  A  man  sold  a  farm  for  $9675;  this  was 
$1465  more  than  he  paid  for  it.  How  much  did 
he  pay  for  the  farm? 

2.  Bertha  sold  a  chicken  and  a  duck;  for  the 
chicken  she  received  25^;  for  the  duck  she  re- 
ceived 10^  more  than  she  did  for  the  chicken;  for 
both  she  received  . 

(b)  A  man  sold  a  cow  and  a  horse;  for  the  cow 
he  received  $37.50;  for  the  horse  he  received 
$24.50  more  than  he  received  for  the  cow.  How 
much  did  he  receive  for  both? 

3.  Helen  spent  8^  for  paper,  4^  for  a  pencil, 
and  had  13^  remaining.  Before  she  bought  the 
paper  and  pencil  she  had  . 

(c)  Mr.  Lewis  spent  $124.50  for  clothing, 
$275.40  for  groceries,  and  had  $134.10  remaining. 
How  much  had  he  before  he  purchased  the  cloth- 
ing and  groceries? 

(d)At  $2.75  a  ]3air,  how  much  will  9  pairs  of 
shoes  cost? 

(e)  From  379.4  subtract  143.25. 

(f )  From  536.74  subtract  272|. 
(g)From  472.37  subtract  148.19. 


218  ELEMENTARY    ARITHMETIC. 

MEASUREMENTS. 

1.  A  cube  has  square  faces.    The  area  of 

each  face  of  a  two-inch  cube  is square  inches. 

The  area  of  all  the  faces  of  a  two-inch  cube  is 

square  inches. 

2.  The  area  of  each  face  of  a  three-inch  cube  is 
square  inches.    The  area  of  all  the  faces  of  a 


three-inch  cube  is  square  inches. 

3.  Can  you  take  your  pencil  and  find  the  area 
of  all  the  faces  of  a  4-inch  cube?  of  a  5-inch  cube? 
of  a  6-inch  cube? 

4.  Henry  has  a  box  that  is  5  inches  long,  3 
inches  wide,  and  2  inches  high. 

( 1 )  The  area  of  the  top  of  the  box  is square 

inches. 

(2)  The  area  oi  tne  bottom  of  the  box  is -. 

(3)  The  area  of  the  top  and  bottom  is  . 

(4)  The  area  of  one  side  of  the  box  is  . 

(5)  The  area  of  both  sides  of  the  box  is  . 

(6)  The  area  of  one  end  of  the  box  is . 


(7)  The  area  of  both  ends  of  the  box  is  . 

(8)  Can  you  tell  without  your  pencil  the  area  of 
the  entire  outside  of  the  box? 

(a)  Multiply  246^  by  T.       (b)  436  x  2|  == 
(c)  Multiply  243  by  32.         (d)  243  -  3.2  = 

(e)  Multiply  $8.75  by  5.  (f)  $3.62  -^7  = 
(g)  Multiply  525  by  24.  (h)  525  x  2.4  - 
(i)  Multiply  144  cubic  inches  by  5. 


PART    IV.  219 

MEASUREMENTS. 

1.  Imagine  a  1-foot  cube.     It  has  faces. 

Each  face  is  a  1-foot .    The  area  of  the  entire 

surface  of  the  cube  is  square  feet. 

2.  Imagine  a  2-foot  cube.     It  has  faces. 

Each  face  is  a  square.      The   area  of  each 

face  is  square  feet.     The  area  of  the  entire 

surface  of  the  cube  is  square  feet. 

3.  The  top  of  a  desk  is  3  feet  wide  and  4  feet 
long;  its  area  is  square  feet. 

4.  A  bLackboard   is  4  feet  wide  and   10   feet 
long ;  its  area  is  square  feet. 

5.  A  rug  is  6  feet  wide  and  8  feet  long;  its 
area  is  square  feet. 

(a)  (b)  (c) 

553  times  1825  times  1544  times 


;5)$2765  $.3)$54T.5 
25  3 

26~  24 

25  24 


15  7 

15  6 


1.5 
1.5 


1)$61.T6 
4 

21 
20 

1.7 
1.6 

.16 
.16 

(d)  Divide  $4735  by  $5.  (e)  $346.5  -  $.5: 

(f)  Divide  $56.25  by  $.05.       (g)  $785  -  $.5  .- 
(h)  Divide  $86  by  $.05.  (i)   $57  -  $.5  = 


220 


ELEMENTARY    ARITHMETIC. 


RATIO    AND    PROPORTION. 


9^ 


12  CGDtS. 


1.  If  6  pears  are  worth  9^,  8  pears  are  worth 
-  cents. 

9  is of  12. 


2. 


6  is  - 

15  is 

18  is 


of  8. 

-  of  20. 

-  of  24. 


12  is 

8  is 

20  is 
24  is 


of  9. 
of  6. 

of  15. 

of  18. 


4.  30^  pays  for  12  lemons;  40^  pays  for 

5.  15^  pays  for  6  oranges;  20^  pays  for 


(a) 

$553 

5)$2765 
25 

26 
25 


15 
15 


(b) 

$182.5 
3)$547.5 

o 
O 

24 

7 
6_ 

1.5 
1.5 


$15.44 

4)$61.76 
_4 

"21 
20 

1.7 
1.6 

.16 
.16 


(d)  Divide  $3265  by  5.         (f)  $4722  -  3  : 

(e)  Divide  $184.8  by  4.        (g)  $573.2  -  2 


PART  IV.  221 


RATIO    AXD    PROPORTION. 


1.  Helen  has  75^;  Bertha  has  50^;  if  Helen 
can  buy  12  yards  of  ribbon,  Bertha  can  buy  . 

2.  Roy  has  15^;  David  has  20^;  if  Roy  can 
buy  12  oranges,  David  can  buy  . 

3.  If  3  horses  consume  60  ears  of  corn  in  a 
day,  4  horses  will  consume  . 

4.  If  Willie  can  earn  24  cents  in  3  hours,  in  4 
hours  he  can  earn  . 

5.  If  a  man  can  earn  $15  in  6  days,  in  8  days 
he  can  earn  . 

6.  If  12  lb.  of  nails  cost  30^,  at  the  same  rate 
16  lb.  will  cost  cents. 

7.  If  20  eggs  are  worth  18^,  30  eggs  are  worth 
cents. 

8.  Six  ponies  consume as  many  oats 

in  a  day  as  8  ponies.     If  8  ponies  consume   20 
quarts,  6  ponies  consume  quarts. 

9.  A  man  can  earn  times  as  much  money 

in  eight  days  as  he  can  in  6  days.     If  he  can  earn 
$21  in  6  days,  in  8  days  he  can  earn  ■ — — . 

10.  If  15  lbs.  of  sugar  are  worth  60^,  20  lbs. 


^t^ti  wuiLii 

ADDITION. 

(a) 

(b)                      (c) 

(d) 

346| 

478|                 3511- 

1361 

175^ 

243                    246 

241 

242 

187A               184A 

826f| 

222  ELEMENTARY    ARITHMETIC. 

MISCELLANEOUS    PROBLEMS. 

1 .  A  pencil  cost  5^ ;  a  book  cost  6  times  as 
much  ;  both  together  cost  ■. 

(a)  A  harness  cost  $17.25  ;  a  carriage  cost  5 
times  as  much.     Find  the  cost  of  both. 

2.  If  5  sheep  cost  $21,  at  the  same  rate  10 
sheep  will  cost  dollars. 

(b)  If  5  tons  of  bran  cost  $62.50,  at  the  same 
rate  how  much  will  10  tons  cost  ? 

3.  If  5  bushels  of  apples  cost  $2.20,  at  the 
same  rate  15  bushels  Avill  cost  . 

(c)  If  5  tons  of  flour  cost  $140.25,  how  much 
will  15  tons  cost  at  the  same  rate  ? 

(d)  Find  the  sum  of  six  thousand  two  hundred 
forty-two,  one  thousand  eighty  four,  and  seven 
hundred  ninety-four. 

4.  Arthur's  book  cost  25^;  his  slate  cost  10^ 
less  than  his  book  cost ;  his  slate  and  book  together 
cost  . 

(e)  A  man  paid  $5650  for  a  house ;  for  a  piece 
of  land  he  paid  $1000  less  than  he  paid  for  the 
house.  How^  much  did  the  land  and  house  to- 
gether cost? 


SUBTRA 

CTION. 

(a) 

(b) 

(c) 

(d) 

4325 

2371 

4628 

3626 

1816 

1528 

2819 

1819 

PART  IV.  223 


SIMPLE    NUMBERS. 


(a)  (b)  (c)  (d)  (e) 

$3)$36  3)$36       7^)35^        7)35^       i)8 


12  times       $12  5  times       5^  16 

1.  In  problem  (a)  the  dividend  is  -,  the 

quotient  is  ;  the  divisor  is  . 

2.  In  problem  (b)  the  quotient  is  ;  the 

dividend  is  ;  the  divisor  is  . 

3.  In  problem   (c)    the    divisor    is  ;  the 

quotient  is  ;  the  dividend  is  . 

4.  In  problem  (d)  the  and  the  are 

like  numbers. 

5.  In  problem  (c)  the  and  the  are 

like  numbers. 

6.  In  a  problem,  the  divisor  is    $3    and  the 
quotient,  10;  the  dividend  is  . 

7.  In  a  problem,  the  dividend  is  $36  and  the 
quotient,  $9  ;  the  divisor  is  . 

8.  If  the  divisor  is  1,  the  quotient  number  is 
the  same  as  the  dividend  number.     If  the  divisor 

is  more  than  1,  the  quotient  number  is  than 

the  dividend  number.     If  the  divisor  is  less  than 

1  the  quotient  number  is  than  the  dividend 

number. 

MULTIPLICATIOX. 
(f)  (g)  (10  (i) 

326     143     234     245 
24      23      32      42 


224  ELEMENTARY    ARITHMETIC. 

DENOMINATE    NUMBERS. 

1.  From  a  can  containing  15  qt.  of  milk,  a 
dealer  sold  5  qt.  1  pt. ;  there  remained . 

(a)  From  425  qt.,  subtract  127  qt.  1  pt. 

2.  A  milk  dealer  sold  2  qt.  1  pt.  to  his  first  cus- 
tomer, 3  qt.  1  pt.  to  his  second  customer,  and  1  qt. 
1  pt.  to  his  third  customer;   to  all  he  sold  . 

(b)  Add  25  qt.  1  pt.,  15  qt.  1  pt.,  and  22  qt.  1  pt. 

3.  From  a  string  5  yd.  long,  George  cut  off  2 
yd.  2  ft.;  there  remained  . 

(c)  From  345  yd.,  subtract  82  yd.  and  2  ft. 

4.  From  a  piece  of  cheese  weighing  6  lb.  a, 
grocer  cut  off  1  lb.  12  oz.;  there  remained  , 

(d)  From  89  lbs.  subtract  17  lbs.  5  oz. 


(e)  (f)  (g) 

258  times  215  times  317  t's. 


;25)$6450  $2.5)$537.5  $.25)$79.25 
50                        50  75 

145  37  I^ 

125  25  2.5 


200  12.5  1.75 

200  12.5  1.75 


(h)  Divide  $6125  by  $25.   (i)    $2875- $25  = 
(j)  Divide  $337.5  by  $2.5.  (k)  $712.5-$2.5  = 
(1)  Divide  $84.50  by  $.25.  (m)  $55.50- $.25  = 


PART  IV.  225 

COMMON    FRACTIONS. 

thirds  sixths  ninths  eighteenths 

1.  One  third  is  eighteenths. 

2.  One  sixth  is  eighteenths. 

3.  One  ninth  is  eighteenths. 

4.  Two  ninths  are  eighteenths. 

5.  One  sixth  and  1  eiorhteenth  are  . 


6.  One  sixth  less  1  eighteenth  are  - 

7.  Five  ninths  and  1  eighteenth  are 

8.  Five  ninths  less  1  eighteenth  are 

Q5_l3_  5_3_ 

10.  11  X  2  =  12  X  I  = 

11.  12x2|=  |-^A  = 

12.  2-1-  1-2  = 


(a)  (b)  (c) 

1258  $21.5  $3.17 

25)16450  25)$537.5  25)$79.25 

50  50  75 

145  37  4.2 

125  25  2.5 

200"  12.5  1.75 

200  12.5  1.75 

(d)  Divide  $3250  by  25.  (e)  $8125  -^  25  : 
(f)  Divide  $572.5  by  25.  (g)  $547.5  -  25 
(h)  Divide  $61.75  by  25.    (i)  $83.50  -  25 


226  ELEMENTARY    ARITHMETIC. 


COMMON    FRACTIONS. 

1.  Add  4  and  -^.  (Eeduce 

2.  Add  -^  and  |-.  (Eeduce 


3.  From  |-  subtract  -^-^.     (Eeduce  

4.  From  |-  subtract  4-       (Eeduce  

5.  Multiply  12  by  2|.      (2  times  

6.  Multiply  51  by  6.         (6  times  

7.  Divide  8|  by  2.  (|-  of  .) 

8.  Divide  2|  by  |.  (Find  how  many  times,  etc.) 

9.  Find  the  sum  of  7^-  and  7^. 

10.  Find  the  sum  of  4^"^^^  and  3|. 

11.  Find  the  difference  of  8  and  2|-. 

12.  Find  the  diiference  of  9^  and  4y^^. 

13.  Find  the  product  of  9  mi>lti]3lied  by  2|. 

14.  Find  the  product  of  2|  multiplied  by  9. 

15.  Find  the  quotient  of  f  divided  by  6. 

16.  Find  the  quotient  of  6|  divided  by  f . 


(a) 

(b) 

ADDITION. 

(d) 

(e) 

24 

35 

46 

56 

24 

32 

24 

21 

46 

34 

41 

31 

38 

36 

44 

55 

42 

20 

26 

84 

47 

56 

34 

16 

24 

38 

38 

47 

66 

74 

PART  IV.  22 


.u^^  i 


MISCELLANEOUS    PROBLEMS. 

1.  A  dealer  sold  6  bushels  of  oats  for  $1.80; 
tlie  price  per  bushel  was  . 

(a)  A   farmer    sold    25    bushels    of   wheat   for 
$18.75.     What  was  the  price  per  bushel  ? 

2.  Eight  bushels  of  beans  are  worth times 

as  much  as  6  bushels.     If  6  bushels  are  worth  $7, 
8  bushels  are  worth  dollars. 

3.  Eight  bags  of  salt  are  worth  — —  times  as 
much  as  6  bags.  If  6  bags  are  worth  $5,  8  bags 
are  worth  dollars. 

4.  Twelve  bushels  of  corn  are  worth times 

as  much  as  8  bushels.     If  8  bushels  are  worth  $3, 
12  bushels  are  worth  dollars. 

5.  Henry's  father  is  6  feet  1  inch  in  height; 

Henry  is  4  feet  9  inches ;  Henry's  father  is  

taller  than  Henry. 

(b)  From  75  ft.  2  in.  subtract  43  ft.  8  in. 

6.  Alice  has  a  picture  that  is  1  ft.  6  in.  wide 
and  2  ft.  4  in.  long ;  its  perimeter  is . 

(c)  What  is  the  perimeter  of  the  floor  of  a  room 
that  is  14  ft.  6  in.  wide  and  16  ft.  8  in.  long  ? 

SUBTRACTION. 


(d)  (e)  (f)  (g)  (li) 

828|         954  425.2        48.75         38.1 

182tV       1821-1-       131.8        29.08         19.6 


228  ELEMENTARY    ARITHMETIC. 

MEASUREMENTS. 

1.  A  rectangle  -^  of  an  inch  wide  and  10  inches 
long  contains  square  inches. 

(a)  A  rectangular  piece  of  land  is  4^  of  a  foot 
wide  and  238  feet  long.  How  many  square  feet 
does  it  contain? 

2.  A  rectangle  2  feet  wide  and  2  yards  long 
contains  square  feet. 

(b)  A  rectangular  piece  of  land  2  feet  wide  and 
35  yards  long  contains  how  many  square  feet? 

3.  A  rectangle  contains  18  square  inches;  it  is 
6  inches  long;  it  is  inches  wide. 

(c)  A  rectangular  piece  of  land  contains  726 
square  feet;  it  is  6  feet  wide.     How  long  is  it? 

4.  Think  of  a  room  that  is  12  feet  long,  10  ft. 
wide,  and  8  feet  high.  Is  it  a  large  or  a  small 
room?  Could  your  teacher  standing  on  the  floor 
of  such  a  room,  reach  the  ceiling? 

(1)  The  area  of  the  ceiling  is  square  feet. 

(2)  The  area  of  the  floor  is  square  feet. 

(3)  The  area  of  one  end  wall  is  . 

(4)  The  area  of  one  side  wall  is  . 


MULTIPLICATIOJN 

"• 

(d) 

(e) 

(f) 

(g) 

(h) 

372A 

575 

326 

47.05 

26.2 

6 

H 

32 

3 

n 

PART  IV.  229 

ME  AS  U  RE  MEN  TS . 

1.  An  oblong  1  inch  wide  and  12  inches  long 

contains  square  inches.     It  is of 

a  square  foot. 

2.  An  oblong  3  inches  wide  and  12  inches  long 

contains  square  inches.     It  is of 

a  square  foot. 

3.  Twenty -four  square   inches   are 

of  a  square  foot. 

4.  Forty-eight  square  inches  are of 

a  square  foot. 

5.  An  oblong  6  inches  wide  and  12  inches  long 

contains  square  inches.     It  is of 

a  square  foot. 

6.  A  rectangle  6  in.  by  6  in.  contains  sq. 

inches.     It  is of  a  sq.  foot. 

7.  Sixty   square    inches    are of    a 

square  foot. 

8.  Eighty-four  square  inches  are of 

a  sq.  foot. 

9.  An  oblong  3  inches  wide  and  4  inches  long 


contams  square  mches.     It  is  - 

of 

a  square  foot. 

DIVISION. 

(a)                  (b)                   (c) 

(d) 

30168*       |.06)$8.34        6)$8.34 

|0.4)$11. 

(e)  Divide  seventy-five  and  forty-five  hundredths 
by  five  hundredths. 

*Change  3i  and  168  to  halves- 


230  ELEMENTARY    ARITHMETIC. 


ADDITION. 

(a) 

(b) 

(c) 

(d) 

(e) 

734| 

674> 

74.3 

24.35 

65.2 

48 

132 

156 

6.07 

74.8 

35H 

356] 

17 

21.4 

53.5 

123 

47 

842.5 

8.25 

87.6 

246A 

1874 

7.2 

'36.36 

95.3 

75 

84 

155 

5.5 

42.7 

(f )  Add  twenty-four  and  seven  tenths,  and  eight 
and  forty-three  hundredths. 


SUBTRACTION. 

(g) 

(10 

(i) 

(J) 

(k) 

6431 

954 

725 

34.76 

89.1 

171| 

3281 

186.2 

18.29 

42.8 

(1)  From   twenty-five    and    eiglit   tentlis,    take 
twelve  and  five  lumdredths. 


MULTIPLICATIO: 

N-. 

(m) 

(n) 

(0) 

(P) 

(q) 

324A 

482 

534 

6.25 

2.75 

6 

71 

231 

5 

8 

(r)  Multiply  nine  and  four  hundredths  by  six. 

(s)  Divide  246.25  by  25. 
(t)  Divide  14568  by  12. 
(u)  Divide  32750  by  25. 


PART  IV.  231 


ADDITION. 


(a)  (b)  (c)  (d) 

308|         506|         75.4         25  bu.  2  pk. 
64|  871        31.8         34  bu.  2  pk. 


SUBTRACTION. 


(a)  (b)  (c)  (d) 

187|        274-1-        35.6         54  bu. 
38^V       146  f         20.8  31  bu.  3  pk. 


MULTIPLICATION. 


(a)  Multiply  54  by  32.  (b)  54  x  3.2  = 
(c)  Multiply  53  by  35.       .    (d)  53.5  x  35  = 

(e)  Multiply  53|  by  35.  (f )   54.3  x  35  = 

(g)  Multiply  454  by  24.  (h)  45.5  x  24  = 

(i)  Multiply  48  by  25-^.  (j)    48  x  25.5  = 

(k)  Multiply  56  by  23|.^  (1)    56  x  23.2  = 

(m)Multiply  64  by  18|.  (n)  64  x  18.7  = 

(o)  Multiply  86  by  21|.  (p)  86  x  21.5  - 


DIVISION. 


(a)  Divide  2106  by  26.  (b)  220.8  -  24 

(c)  Divide  1272  by  24.  (d)  687.5  -  25 

(e)  Divide  4150  by  25.  (f )  57.46  -  26 

(g)  Divide  8372  by  26.  (h)  31.75  -  25 

(i)  Divide  5842  by  23.  (j)  637.2  -  27 

(k)  Divide  8235  by  27.  (1)  820.8  -  27 

(m)  Divide  6345  by  27.  (n)  63.18  -  27 

(o)  Divide  8475  by  25.  (p)  94.25  -  25 


23^  ELEMENTARY    ARITHMETIC. 

For  dictation  exercises  in  addition,  subtraction, 
multiplication,  and  division.* 


(a) 

(b) 

(c) 

(d) 

^  (6240 
*  t  3760 

3675 

5272 

3852 

6325 

4728 

6148 

2  l^^2^ 

'  14680  . 

4354 

3904 

4266 

5646 

6096 

5734 

3  P4^^  ■ 
'  [2540 

7532 

7384 

5058 

2468 

2616 

4942 

f4020 

'  (5980 

5831 

3272 

6282 

4169 

6728 

3718 

(1960 
■  1 8040 

6202 

4352 

7506 

3798 

5648 

2494 

a   |2520 

1  7480 

2947 

5376 

3528 

7053 

4624 

6472 

7  i'3740 
'  [6260 

8274 

4200 

2358 

1726 

5800 

7642 

8  1^^^^ 
'  1 1480 

7385 

6736 

8172 

2615 

3264 

1828 

[5520 

'  1  4480 

5467 

8296 

3726 

4533 

1704 

6274 

^^  (7660 
12340 

4445 

2776 

5544 

5555 

7224 

4456 

*  See  "  Suggestions  to  Teachers,"  pp.  247  and  248. 


DEFINITIONS   AND   EXPLANATIONS.^^ 

A  unit  is  one. 

A  number  is  one  or  it  is  composed  of  ones. 
Notation  is  tlie  art   of   expressing  numbers  by 
figures  or  other  characters. 

ARABIC    NOTATION. 

In  the  Arabic  Notation  figures  are  employed. 
The  figures  are:  1,  2,  3,  4,  5,  6,  7,  S,  9,  0. 

In  the  number  29,  the  figure  9  is  said  to  stand  in  the 
first  place  and  the  figure  2  in  the  second  place. 

In  the  number  437,  the  figure  7  is  said  to  stand  in  the 
first  place,  the  figure  3  in  the  second  place,  and  the  figure 
4  in  the  third  place. 

In  the  number  8156,  the  figure  6  is  said  to  stand  in  the 
first  place,  the  figure  5  in  the  second  place,  the  figure  1  in 
the  third  place,  and  the  figure  8  in  the  fourth  place. 

A  figure  in  the  first  place  expresses  units. 

A  figure  in  the  second  place  expresses  tens. 

A  figure  in  the  third  place  expresses  hundreds. 

A  figure  in  the  fourth  place  expresses  thousands. 

A  figure  in  the  fifth  place  expresses  tens  of  thousands. 

In  the  number  4.65,  the  figure  6  is  said  to  be  in  the  first 
decimal  place,  the  figure  5  in  the  second  decimal  place. 

A  figure  in  the  first  decimal  place  expresses  tenths. 

A  figure  in  the  second  decimal  place  expresses  hundredths. 

Tell  what  each  figure  expresses  in  the  following 
combination :  2764.35. 

*See  that  the  pupil  can  read  the  following  pages  intelligentl>' 
before  he  is  asked  to  commit  to  memory  any  part  of  them. 

233 


234  ELEMENTARY   ARITHMETIC. 


ADDITION. 


Addition  is  the  process  of  uniting  two  or  more 
numbers  into  one  number. 

The  sum  is  the  number  obtained  by        26 
adding.  Z^ 

75  (Sum.) 

SUBTRACTION. 

Subtraction  is  the  process  of  taking  one  number 
from  (out  of)  another  number. 

The  minuend  is  the  number  from  which  another 
number  is  taken. 

The  subtrahend  is  the  number      $75  (Minuend.) 
taken  from  another  number.         $38  (Subtrahend.) 

The  difference  is  the  number      $37  (Difference.) 
obtained  by  subtracting. 

Observe  that  the  sum  of  the  subtrahend  and  difference 
equals  the  minuend.* 

MULTIPLICATION. 

Multiplication  is  the  process  of  taking  one  number 
as  many  times   as  there    are 

units  in  another  number.  $36  (Multiplicand.) 

The  multiplicand  is  the  num-  25  (Multiplier.) 

ber  taken,  or  repeated.  $180 

The  multiplier  is  the  number  ^72 

that  shows  how   many  times  $900  (Product.) 
the  multiplicand  is  to  be  taken, 
or  repeated. 

*  Teach  pupils  to  "prove"  their  problems  in  subtraction. 


DEFINITIONS    AND    EXPLANATIONS.  235 

The  product  is  the  number  obtained  by  multij)ly- 
ing. 

In  the  example  given,  $180  and  $720  ai-e  called  the 
partial  (part)  products.  $180  is  the  product  of  $36  and 
5;  $720  is  the  product  of  $36  and  20. 

Observe  that  dividing  the  product  by  the  multiplier 
gives  the  multiplicand.* 

DIVISION. 

Division  is  one  of  tioo  processes. 
I.  It  is  finding  how  many  times  one  number  is 
contained  in  another  number;  $18  -^  $2  =  9. 

II.  It  is  finding  one  of  the  equal  parts  of  a 
number;  $18 -- 2  =  $9. 

To  divide  $18  by  $2  means  to  separate  $18  into  groups  of 
$2  each  and  count  the  groups.  To  divide  $18  by  2 
means  to  separate  $18  into  2  equal  groups,  and  count 
the  dollars  in  one  group;  that  is,  find  one  half  of  $18.  In 
Case  I.  the  quotient  tells  how  many  times  the  divisor  is 
contained  in  the  dividend.  In  Case  II.  the  quotient  is  a 
part  of  the  dividend. 

To  THE  Teacher. — The  second  case  is  often  very  properly 
called  partition.  But  both  processes  are  evidently  cases 
of  division,  since  in  both  instances  we  separate  (divide) 
the  given  number  into  equal  parts.  In  Case  I.  we  count 
the  parts  (groups).  In  Case  II.  we  count  the  units  in 
each  part  (gxoup). 

The  dividend  is  the  number  divided  or  separated. 
The  divisor  is  the  number  by  which  we  divide. 
The  quotient  is  the  number  obtained  by  dividing, 

*  Teach  pupils  to  "  prove  "  their  problems  in  multiplication. 


236  ELEMENTARY    ARITHMETIC. 

Observe  that  in  either  case  the  product  of  the  divisor 
and  quotient  equals  the  dividend.* 

To  THE  Teacher. — There  can  be  no  remainder  in  a  com- 
plete division.  Therefore,  the  product  of  the  quotient 
and  divisor  is  ahvays  equal  to  the  dividend.  We  may 
have  a  remainder  when  the  process  of  dividing  is  incom- 
plete. In  such  a  case  the  quotient  is  incomplete  and  the 
remainder  is  the  undivided  part  of  the  dividend.  To 
the  product  of  the  incomplete  quotient  and  divisor  add 
the  remainder,  and  the  sum  thus  obtained  will  be  equal 
to  the  dividend. 

An  even  number  is  the  number  two,  or  a  number  that 
can  be  separated  into  twos ;  as,  4,  6,  20,  40,  44,  etc. 

A  number  that  cannot  be  exactly  separated  into  twos  is 
called  an  odd  number :  as,  3,  5,  7,  21,  71,  etc. 


FRACTIONS. 

A  fraction  is  one  or  more  of  the  equal  parts  of  a 
unit. 

A  fraction  is  usually  expressed  by  two  numbers, 
one  of  them  being  written  above  a  short  horizontal 
line  and  the  other  below  it;  thus,  |^,  |,  fV- 

The  number  above  the  line  is  called  the  numerator. 

The  number  below  the  line  is  called  the  denomi- 
nator. 

The  denominator  shows  the  number  of  equal 
parts  into  which  the  unit  is  divided. 

*  Teach  the  pupils  to  "  prove"  their  problems  in  divlBion. 


DEFINITIONS    AND    EXPLANATIONS.  237 

The  numerator  shows  the  number  of  parts 
taken. 

The  denominators  of  some  fractions  are  not 
usually  expressed  by  figures;  thus,  5  tenths  is 
usually  written,  .5;  27  hundredths  is  usually  writ- 
ten, .27. 

Of  the  fraction  |,  7  is  the  numerator  and  8  is 
the  denominator. 

Of  the  fraction  .5,  5  is  the  numerator  and  10  is 
the  denominator. 

Of  the  fraction  .27,  27  is  the  numerator  and  100 
is  the  denominator. 

If  the  numerator  and  the  denominator  of  a  frac- 
tion are  the  same  number,  as  -|,  ^l?  w?  ^^^•:>  ^^^^ 
fraction  is  equal  to  one  unit. 

If  the  numerator  of  a  fraction  is  greater  than 
the  denominator,  as  f,  l^,  \^-,  etc.,  the  fraction  is 
equal  to  more  than  one  unit. 

A  fraction  whose  numerator  is  equal  to  or 
greater  than  its  denominator  is  called  an  improper 
fraction. 

A  fraction  whose  numerator  is  less  than  its 
denominator  is  called  a  proper  fraction. 

Two  thirds,  f,  |-,  |-^,  are  proper  fractions. 

Five  fourths,  |^,  |,  ff,  are  improper  fractions. 


238  ELEMENTARY   ARITHMETIC 

DRY    MEASURE. 

2  pints  (pt.)  =  1  quart  (qt.). 
8  quarts  =  1  peck  (pk.). 
4  pecks  =  1  bushel  (bu.). 


LIQUID    MEASURE. 

2  pints  (pt.)  =  1  quart  (qt.). 
4  quarts  =  1  gallon  (gal.). 


MEASURE    OF    TIME. 

60  seconds  (sec.)  =  1  minute  (niin.)o 

60  minutes  =  1  hour  (hr.). 

24  hours  =  1  day  (da.). 

7  days  =  1  week  (wk.). 

28  to  31  days  =  1  month  (mo.). 

12  months  =  1  year  (yr.). 

365  days  =  1  common  year. 

366  days  =  1  leap  year. 

52  weeks  and  1  day  =  1  common  yeaFo 
52  weeks  and  2  days  =  1  leap  year. 


LINEAR    MEASURE. 


12  inches  (in.)  =.  1  foot  (ft.). 
3  feet  =  1  yard  (yd.). 


DEFINITIONS   AND   EXPLANATIONS.  239 


AVOIRDUPOIS    WEIGHT. 


16  ounces  (oz.)  =  1  pound  (lb.). 
2,000  pounds  =  1  ton(T.). 


SQUARE    MEASURE. 


144  square  inches  (sq.  in.)  =  l  square  foot  (sq.  ft.), 
9  square  feet  (sq.  ft.)  =  1  square  yard  (sq.  yd.). 


ROMAN    NOTATION. 


In  the  Roman  Notation  seven  capital  letters  are 
emj)loyed.     The  letters  are — I,  V,  X,  L,  C,  D,  M. 
I.  =  1,  V.  =  5,  X.  =  10,  L.  =  50,  C.  -  100, 


D.  =  500,  M.  =  1000. 


PRINCIPLES. 


When  a  letter  is  repeated  its  value  is  repeated.  XX.  =  20. 
II.  =  2. 

When  a  letter  is  placed  before  one  of  greater  value,  the 
difference  of  their  values  must  be  taken.  IX.  =  ( 10  —  1 )  =  9. 

When  a  letter  is  placed  betAveen  two  letters  each  of 
greater  value,  its  value  is  taken  from  the  last  letter. 
XIX.  =3  10  -f  10  -  1  =  19. 

Placing  a  short  horizontal  line  over  a  letter  multiplies 
its  value  by  1000.     X.  =  10,000. 

Sometimes  small  letters  are  employed  instead  of  capitals ; 
thus,  ii.  =  2,  iv.  =  4,  etc. 


240 


ELEMENTARY    ARITHMETIC. 


ROMAN    NOTATIOX    TABLE. 


II.  =  2. 

III.  =:  3. 

IV.  =  4 

V.=:5. 
VI.  :=  6. 

VII.  =  7. 

VIII.  =  8. 

IX.  =9. 
X.=  10. 
XL  =11. 

XII.  =  12. 

XIII.  =  13. 

XIV.  =  14. 

XV.  =  15. 

XVI.  =  16. 

XVII.  =  17. 

XVIII.  =  18. 

XIX.  =  19. 

XX.  =  20. 


XXX.  =  30. 
XL.  =  40. 
L.=  50. 
LX.=  60. 
LXX.  =  70. 
LXXX.  =  80. 
XC.=  90. 
C.=  100. 
CO.  =  200. 
CCC.=  300. 
CCCC.  =  400. 
D.=  500. 
DC.  =  600. 
DCC.=  700. 
DCCC.  =  800. 
DCCCC.=  900. 
M.=  1000. 
MM.  =  2000, 
V.=  5000. 


XXXVIIL  = 

XLVI.  = 

MDCC.  = 

XCIX.  = 

CCCVL  = 

DXLV.  = 

XXIV.  = 

LXXXIV.  = 

LXXVI.  = 

XL  VII.  = 

XXXII.  = 

XCVII.  = 

LVIIL  = 

CCXIX.  = 

DXIX.  = 

MXIX.  = 

LXXXI.  = 

LXIV.  = 

MDCCC.  = 


MDCCCXCVL  = 


The  author  of  this  book  was  born  Feb.  IX.,  in  the  year 
of  our  Lord  MDCCCXLI. 

The  Roman  notation  is  now  chiefly  employed  in  num- 
bering chapters  or  lessons,  in  dates,  and  upon  the  dials  of 
time-pieces. 

How  is  the  number  four  represented  upon  the  face  of  a 

clock  ? 

*A  period  is  usually  placed  after  each  completed  Roman 
numeral. 


SUGGESTIONS   TO   TEACHERS. 

Read  the  preface  of  this  book.  Read  pages  5  and  6,  and  see 
that  pupils  are  familiar  with  the  number  facts  there  presented 
before  they  are  required  to  bring  the  book  to  the  schoolroom. 
But  even  after  the  book  is  in  the  hands  of  the  pupil,  he  should 
not,  as  a  rule,  be  asked  to  read  a  page  until  the  teacher  has 
assured  herself  that  he  is  thoroughly  prepared  for  it.  The  pupil 
cannot  prepare  himself.  It  is  the  business  of  the  teacher  not 
simply  to  "hear  recitations,"  but  to  teach.  The  teaching  to  be 
done  in  connection  with  a  page  of  this  book,  should  be  done 
mainly  before  the  pupil  attempts  to  read  it.  This  teaching  is  the 
leading  of  the  pupil  to  perceive  those  magnitude  relations  and  to 
memorize  those  primary  number  facts  which  are  necessary  to  be 
perceived  and  memorized  in  order  that  the  pupil  may  be  able  to 
read  the  pages.  Until  the  teacher  can  devise  a  better  plan  for 
herself,  she  should  adhere  strictly  to  the  following  order  of 
procedure: 

STEP   I. 

The  teacher  takes  the  book.  The  pupils  are  without  books 
and  give  their  undivided  attention  to  the  teacher.  The  teacher 
reads  one  of  the  statements,  pausing  at  the  blank  for  the  pupils  to 
supply  the  necessary  word  or  w^ords.  Pupils  signify  their  readi- 
ness to  answer  by  raising  their  right  hands.  The  teacher  names 
the  pupil  who  is  to  give  the  words  to  be  supplied.  (Occasionally, 
especially  if  the  problems  seem  difficult,  a  pupil  may  come  for- 
ward briskly  and  whisper  his  answer  to  the  teacher.  Another 
and  another  may  follow  rapidly  until  all  who  are  prepared  to  do 
so  have  given  answers.  This  promotes  independence  and  enables 
the  teacher  better  to  judge  of  individual  work).  If  the  teacher 
discovers  that  there  are  primary  number  facts  introduced  on  the 
page  w^hich  have  not  been  memorized  by  the  pupil,  this  should 
be  attended  to  at  once.  Do  not  proceed  until  this  has  been 
thoroughly  accomplished.  Better  spend  several  days,  if  neces- 
sary, in  the  preparation  for  reading  a  single  page,  than  to  attempt 
to  read  it  without  proper  preparation. 

STEP   II. 

See  that  each  pupil  is  familiar  with  the  written  forms  of  all 
words  appearing  upon  the  page  under  consideration.  Use  the 
blackboard  for  this  purpose  and,  as  a  rule,  show  new  words  in  the 
connection  in  which  they  appear  in  the  book. 

241 


242  ELEMENTARY    ARITHMETIC. 


STEP    III. 


Put  the  book  into  the  hands  of  the  pupils  and  let  them  read 
silently  the  page  for  which  preparation  has  been  made. 

STEP   IV. 

The  pupils  may  now  read  aloud  the  page  which  has  been 
read  silently.  If  the  work  of  preparation  has  been  thoroughly 
done  there  will  be  but  little  hesitation  on  the  part  of  the  pupils 
in  reading  the  page. 

STEP   V. 

The  pupils  may  copy  (filling  the  blanks)  sorne  designated  part 
of  the  page  that  has  been  read.  Allow  no  careless  written  work. 
In  examining  the  papers  make  but  two  classes;  those  that  are 
"perfect"  and  those  that  are  "imperfect."  The  teacher  is  at  fault 
if  more  than  half  the  papers  are  "imperfect,"  In  a  well  taught 
class  often  90  per  cent,  of  the  papers  will  be  "perfect."  In  this 
examination  of  papers,  spelling,  capital  letters,  punctuation,  and 
accuracy  of  result  are  to  be  considered.  If  there  be  a  single  mis- 
spelled word,  or  one  figure  or  punctuation  mark  be  wrong,  the 
paper  must  be  excluded  from  the  "perfect  paper"  class.  If  the 
teacher  finds  it  seemingly  impossible  to  secure  50  to  75  per  cent, 
of  "perfect  papers,"  more  time  should  be  spent  in  preparation  and 
the  amount  of  work  required  of  the  pupil  should  be  diminished. 
Better  a  single  statement  accurately  written  than  a  half  page 
with  many  errors.  The  work  of  the  teacher  should  be  not  mainly 
the  correction  but  the  prevention  of  errors. 

Page  9. — If  the  pupil  is  prepared  to  read  in  a  Third  Reader, 
and  if  the  number  facts  given  on  pages  5  and  6  have  been 
mastered,  he  will  read  this  page  without  much  hesitation.  If  he 
finds  difficulty  in  calling  the  words,  lay  the  book  aside  and  teach 
him  to  read.  If  he  cannot  readily  fill  the  blanks,  teach  him  orally 
the  necessary  number  facts. 

Page  10. — During  the  first  reading  of  this  page  by  the 
teacher  (the  pupils  filling  the  blanks)  each  pupil  should  have  a 
foot  ruler  in  his  hand.  After  this,  it  should  be  read  a  second 
time,  the  ruler  being  hidden  from  view. 

Before  reading  statements  11  and  13,  the  pupils  may  "draw  a 
square  in  the  air"  if  such  a  procedure  is  necessary  to  assist  the 
imaginative  power.  They  must  be  trained  in  every  possible  way 
to  image  magnitude. 

Page  11. — Observe  that  there  are  problems  in  addition  at  the 
bottom  of  this  page,  also  on  pages  16,  21,  26,  31,  36,  etc.,  through- 
out the  book.  So  far  as  practicable,  require  pupils  to  make  these 
additions  ^?^s^  ivithout,  then  with,  the  aid  of  a  pencil.     The  pupil 


SUGGESTIONS    TO    TEACHERS.  243 

should  perceive  the  fact  that  28  and  2  are  30,  before  he  is  allowed 
to  use  his  pencil  to  secure  this  result.  He  should  use  his  pencil 
as  a  preparation  for  more  difficult  additions  in  which  the  pencil 
will  be  a  convenience. 

Page  12. — Observe  that  there  are  problems  in  subtraction  at 
the  bottom  of  this  page,  also  on  pages  17,  22,  27,  32,  37,  42,  etc., 
throughout  the  book.  This  work  should  be  done  in  the  same 
order  as  suggested  for  the  work  at  the  bottom  of  page  11. 

Page  13. — If  the  pupil  cannot  image  the  squares  and  oblongs 
described  on  this  page  the  pencil  or  the  crayon  must  be  used; 
but  sometime  he  must  learn  to  image  such  figures  without  draw- 
ing them.  The  strength  of  the  pupil  depends  very  largely  upon 
his  skill  in  making  accurate  mental  pictures  from  oral  and  written 
descriptions.     This  xooiver  must  he  cultivated  from  the  first. 

Observe  that  there  are  problems  in  multiplication  at  the  bot- 
tom of  this  page,  also  on  pages  18,  23,  28,  33,  38,  etc.,  throughout 
the  book.  So  far  as  practicable,  require  pupils  to  make  these 
multiplications  first  ivithout,  then  with,  the  aid  of  a  pencil.  The 
pupil  should  perceive  the  fact  that  two  35's  are  70,  before  he  is 
allowed  to  use  his  pencil  and  "carry  "  to  secure  this  result. 

Page  14. — Here  the  pupil  should  be  made  somewhat  familiar 
with  the  meaning  and  the  use  of  the  expression,  are  contained  in. 
Observe  that  in  the  problems  at  the  bottom  of  this  page  as  well  as 
in  those  on  pages  19,  24,  29,  34,  39,  44,  49,  etc.,  the  pupil  is 
required  to  find  hoiu  many  times  one  number  of  things  is  con- 
tained in  another  number  of  things. 

Page  15.— Observe  that  in  the  problems  at  the  bottom  of 
this  page  as  well  as  in  those  on  pages  20,  25,  30,  35,  40,  45,  etc.,  the 
pupil  is  required  to  find  one  of  the  equal  parts  of  a  number  of 
things;  thus,  to  divide  12"?  by  2  is  to  find  |  of  12*?.  The  pupil 
should  solve  these  problems  "mentally"  before  using  the  pencil  in 
their  solution. 

Page  16.— During  the  first  reading  of  this  page  by  the  teacher 
(the  pupils  filling  the  blanks)  the  pint  and  quart  measure  may  be 
before  the  pupils.  The  page  should  then  be  read  again,  the 
measures  being  hidden  from  view. 

Page  17.— See  note  under  "Pacts  of  Partition  and  Multipli- 
cation," page  6. 

Page  19.— This  page  should  not  be  attempted  until  the  pupil 
is  familiar  with  the  thermometer  and  its  use.     In  many  schools 


244  ELEMENTARY    ARITHMETIC. 

the  subject  of  temperature  is  presented  in  the  lower  grades. 
Even  primary  pupils  will  take  great  interest  in  a  temperature 
record,  and  will,  with  little  effort  on  the  part  of  the  teacher, 
become  familiar  with  this  class  of  problems. 

Page  30. — This  page  is  designed  to  impress  upon  pupils  the 
double  nature  of  abstract  problems  in  division.  6  divided  by  2, 
may  mean,  find  how  Tiiany  times  2  (apples,  dollars,  cents)  are  con- 
tained in  6  (apples,  dollars,  cents),  or  it  may  mQanfind  ^  of  6 
(apples,  dollars,  cents.) 

Page  31. — The  pupil  who  has  done  the  work  thoroughly  to 
this  point  will  be  able  to  read  this  'page,  filling  all  the  blanks 
correctly,  in  two  minutes  or  less. 

Page  32.^ — Before  proceeding  further,  see  that  each  pupil  has 
so  perfectly  memorized  the  thirty-three  addition  problems  that 
he  can  recite  the  answers  to  them  in  33  seconds  or  less.  Do  not 
require  him  to  name  the  figures,  but  to  give  sums  only. 

Page  35. — Do  not  at  first  use  a  digit  to  represent  the  number 
of  parts  into  which  a  unit  is  divided.  Instead  of  i,  write  one^ 
fourth  or  1  fou7^th. 

Pages  35,  36,  37,  38.— Observe  that  in  solving  the  problems 
on  page  35,  the  pupil  thinks  of  surface  magnitude;  page  36, 
linear  magnitude;  page  37,  value  magnitude;  while  on  page  38, 
all  these  are  presented. 

Page  41. — The  three  number  facts  here  given  mustbeper- 
fectly  memorized.  Pupils  cannot  easily  and  quickly  perceive 
magnitude  relation  without  the  mastery  of  the  primary  number 
facts.  The  more  important  of  these  are  given  on  pages  41,  51,  61, 
71,  81,  91,  101,  111,  121,  131,  141, 151,  and  reviewed  on  page  152. 
See  that  these  facts  are  mastered  when  presented.  Do  not  allow 
it  to  he  truthfully  said  of  your  fourth  grade  pupil  that  he  ''does 
not  knoiD  the  niidtiplication  table." 

Page  45. — Teach  orally  the  facts  given  on  this  page  before 
the  pupil  is  asked  to  read  it.  Put  diagrams  on  the  blackboard 
and  continue  the  oral  work,  if  need  be,  for  several  days,  until  the 
pupil  can  easily  think  one  half,  one  fourth,  one  sixth  of  some 
thing  when  the  words  that  should  suggest  these  are  spoken. 
Success  here,  as  everywhere  in  mathematics,  depends  upon  the 
ability  of  the  pupil  to  b^ing  imaged  magnitude  into  consciousness. 

The  suggestions  given  for  page  45  will  apply  to  pages  55, 65,  75, 
85,  95, 105,  115,  125,  135,  145.     If  the  pupil  is  unable  to  fill  the 


SUGGESTIONS    TO    TEACHERS.  245 

blanks  on  any  one  of  these  pages  promptly,  review  all  similar 
pages  preceding  it.  If  this  does  not  enable  the  teacher  to  secure 
satisfactory  results,  more  oral  work  should  be  done  with  the  dia- 
grams on  the  blackboard  confronting  the  pupil.  The  learner  must 
perceive  that  \  and  ^  are  |;  that  \  and  |-  are  f,  etc. 

Observe  that  each  of  these  pages  provides  problems  in  addition, 
subtraction,  multiplication,  division,  and  "  partition"  of  fractions. 

Page  48. — Regard  the  problems  on  this  page,  particularly 
those  near  the  top  of  the  page,  as  a  test  of  the  quality  of  the  work 
of  the  teacher  and  pupil  while  passing  over  the  preceding  pages 
of  the  book.  Indeed  the  same  may  be  said  with  reference  to 
almost  any  page  in  the  book  after  the  first;  but  this  thought  is 
especially  ai^plicable  to  pages  48,  58,  68,  78,  88,  98. 

Page  53. — Teach  orally  the  meaning  and  use  of  the  word 
perimeter.  Do  the  same  with  other  terms  introduced  on  pages 
63  and  73.  Perfect  familiarity  with  these  terms  and  the  ability  to 
image  such  figures  as  are  mentioned,  are  the  necessary  prepara- 
tion for  the  work  on  pages  83,  93, 103, 113, 123,  133,  143. 

Page  64. — Lead  pupils  to  distinguish  sharply  between  the 
two  kinds  of  problems  given  in  the  first  four  examples.  Ask, 
again  and  again,  when  a  problem  like  one  of  these  is  presented, 
What  does  it  mean  9'^    See  pages  74,  84,  94. 

Page  67. — The  drill  suggested  on  this  page  is  invaluable.  The 
other  steps  of  this  drill  will  be  found  on  pages  77,  87,  97, 107, 117, 
127,  137.  Require  pupils  to  add  numbers  represented  by  figures 
in  a  column,  without  naming  each  number;  thus,  in  adding 
column  (a)  page  67,  the  pupils  will  say,  tico,  four,  six,  eight,  etc. 
Put  columns  similar  to  these  upon  the  blackboard  and  continue 
the  drill  until  the  pupils  can  add  a  column  made  up  of  2's  and  I's, 
or  of  3's,  2's,  and  I's,  almost  as  readily,  as  they  can  add  a  column 
of  2's  or  of  3's. 

Page  70. — On  this  page  tenths  are  presented  for  the  first 
time  without  the  written  denominator.  If  the  pupil  clearly 
understands  that  .4  is  another  way  of  writing  j%,  and  that  2.7  is 
another  way  of  writing  f  ^  or  2  j\,  he  will  readily  do  work  sug- 
gested on  this  page  and  similar  work  found  on  pages  80  and  90. 

Page  89. — If  pupils  are  taught  the  meaning  of  the  different 
problems  on  this  page  they  will  find  no  very  great  difficulty  in 
their  solution.  The  same  may  be  said  of  the  same  class  of  prob- 
lems found  on  pages  96,  99, 106, 109, 116,  119, 126, 136, 146. 


246  ELEMENTARY    ARITHMETIC. 

Page  104. — Be  sure  that  the  pupil  understands  the  meaning 
of  the  work  on  this  page.  Before  he  attempts  to  multiply  by  a 
fraction,  what  it  means  to  do  this,  must  be  made  clear  to  him. 
He  must  not  be  allowed  to  proceed  mechanically  to  obtain  an 
ansiver  while  he  knows  nothing  of  the  magnitude  relation  in- 
volved. To  multiply  by  \  is  to  take  once  |  of  a  magnitude,  that 
is,  ^  of  it;  to  multiply  by  |  is  to  take  three  times  |  of  a  magnitude, 
that  is,  I  of  it. 

Page  109,  Prob.  10.— To  multiply  |  ft.  by  2|,  take  2  times  | 
of  a  foot  and  to  this  add  |  of  |-  of  a  foot.  Prob.  16. — To  multiply 
1.2  in.  by  2|,  take  2  times  1.2  in.  (12  tenths),  to  which  add  |  of  1.2 
in.  (12  tenths). 

Page  114,  Problems  4  and  10.— Remind  the  pupil  that  to 
multiply  by  2|,  he  must  take  2  times  the  multiplicand  and  to  this 
add  ^  of  the  multiplicand.  The  multiplying  of  2|  by  2\  becomes 
a  very  simple  problem  when  the  pupil  understands  ivhat  it  means. 

Page  152. — Do  not  allow  a  pupil  to  begin  the  work  in  Part 
III  of  this  book  until  he  has  memorized  every  number  fact  given 
on  this  page. 

Pages  153  to  172. — Observe  that  these  20  pages  are  devoted 
to  the  solution  of  problems  involving  whole  numbers  and  tenths. 
The  usual  "  spiral "  appears  on  pages  153,  154,  155.  Another 
"  spiral "  covers  pages  156  to  159.  Pages  161  to  161  are  for  the 
purpose  of  teaching  the  multiplication  of  any  integral  number  (of 
things)  by  tenths.  See  that  each  step  in  this  work  is  made  clear 
to  the  pupil.  Review  many  times  if  necessary.  Pages  166  to  170 
are  for  the  purpose  of  making  clear  the  distinction  between  (1) 
dividing  a  number  cf  tenths  (of  things)  by  a  number  of  tenths  (of 
things)  and  (2)  finding  one  of  the  equal  parts  of  a  number  of 
tenths  (of  things).  If  this  work  is  done  as  here  suggested  it  will 
go  a  long  way  in  guarding  the  pupil  against  errors  in  "  pointing 
off  "  in  division  of  decimals. 

Pages  171  and  172. — Note  the  similarity  of  the  numbered 
or  "figure  problems "  to  the  corresponding  "  letter  problems." 
Pupils  who  have  solved  the  figure  problems  in  class,  should  be 
able  to  solve  the  letter  problems  without  assistance,  at  their  seats. 

Page  173. — See  that  the  pupil  understands  that  to  multiply  15 
by  23,  he  may  take  3  times  45,  and  20  times  45,  and  find  their  sum. 

Page  182. — Pupils  should  solve  the  figure  problems  in  class; 
the  letter  problems  without  assistance  at  their  seats. 


SUGGESTIONS    TO    TEACHERS.  247 

Page  188. — Pupils  should  be  reminded,  if  necessary,  that  a 
square  inch  is  a  1-inch  square  or  its  equivalent. 

Pages  193  to  212. — Observe  that  these  pages  are  devoted  to 
the  solution  of  problems  involving  whole  numbers,  tenths,  and 
hundredths.  Review,  if  necessary,  pages  153  to  172.  Compare 
the  following:  Pages  153  and  193;  154  and  194;  155  and  195,  etc. 

Pages  230  and  231.— The  pupil  should  be  expected  to  do 
this  work,  and  to  solve  such  problems  as  may  be  dictated  from 
page  240,  luith  '' xmrfect  accuracy."  Nothing  short  of  this  should 
be  commended  in  mechanical  processes.  To  have  one  figure- 
ivrong  in  one  problem  of  every  ten  is  failure.  "  Ninety  j^er  cent " 
in  such  work  is  neither  ^' excellent"  nor  "good,''  it  is  ivorthless. 
Careless  work  must  not  be  tolerated.  The  accurate  habit  must 
be  established. 

Page  232.— Hundreds  of  problems  may  be  given  by  dictation 
from  this  page,  and  the  teacher  may  know  the  answer  to  each 
problem  with  very  little  effort. 

ADDITION. 

Give  any  integral  number  represented  by  four  figures,  as 
2461,  and  with  this  give  all  the  numbers  in  any  three  groups  on 
the  page;  their  sum  is  32461.  The  same  number  with  any  four 
groups  will  give  42461 ;  with  any  five  groups,  52461,  etc.  In 
giving  the  numbers  in  the  groups,  give  first,  one  from  each  group; 
then,  the  remaining  one  of  each  group.  Of  course  it  is  not  neces- 
sary that  the  number  supplied  by  the  teacher  should  always  be 
given  first. 

SUBTRACTION. 

Take  any  number  greater  than  10000;  from  this  subtract  first 
one  number  of  a  group;  from  the  remainder  subtract  the  other 
number  of  the  group;  the  last  result  should  be  the  given  number 
less  10000.  Take  the  number  15246  ;  subtracting  a&  directed,  the 
last  result  will  be  5246. 

Subtract  either  number  of  any  group  from  10000,  and  the 
result  will  be  the  other  number  of  the  group. 

Subtract  either  number  of  any  group  from  a  number  that  is  2 
or  5  or  25  or  100  or  1000  more  than  10000.  and  the  result  will  be  2 
or  5  or  25  or  100  or  1000  more  than  the  other  number  of  the  group. 

MULTIPLICATION. 

Multiply  any  number  by  3  and  by  7,  or  by  4  and  by  6,  or  by  2 


248  ELEMENTARY    ARITHMETIC. 

and  by  8,  and  the  sum  of  the  two  products  equals  10  times  the 
number. 

Multiply  any  number  by  7  and  by  8  and  the  sum  of  the  two 
products  equals  15  times  the  number,  or  10  times  the  number  plus 
|-  of  10  times  the  number. 

Multiply  any  number  by  12  and  by  58,  or  by  17  and  by  53,  or 
by  36  and  by  61,  and  the  sum  of  the  two  products  equals  100  times 
the  number. 

DIVISION. 

Divide  any  number  by  1  and  by  5  and  by  20,  and  the  sum  of 
the  three  quotients  equals  |  of  the  number. 

Divide  any  number  by  3  and  by  6,  and  the  sum  of  the  two 
quotients  equals  ^  of  the  number. 

Divide  the  numbers  in  any  group  on  the  page  by  7,  and  the 
sum  of  the  two  quotients  is  1428^. 

Divide  the  numbers  in  any  group  on  the  page  by  8,  and  the 
sum  of  the  two  quotients  is  1250. 

Divide  the  numbers  in  any  group  on  the  page  by  9,  and  the 
sum  of  the  two  quotients  is  1111^. 

Each  number  in  column  (a)  is  exactly  divisible  by  2,  by  4,  by 
5,  by  10,  and  by  20. 

The  first  number  of  each  group  in  column  (b)  is  exactly  divis- 
ible by  7. 

The  first  number  of  each  group  in  column  (c)  is  exactly  divis- 
ible by  8. 

The  first  number  of  each  group  in  column  (d)  is  exactly  divis- 
ible by  3,  by  6,  and  by  9, 

If  the  teacher  will  make  herself  thoroughly  familiar  with  the 
foregoing  statements,  she  will  be  able  to  dictate  an  unlimited 
amount  of  practice  work,  and  to  test  the  accuracy  of  the  pupils, 
without  actually  solving  the  problems  herself. 

REVIEW. 

If,  after  the  book  has  been  completed,  the  pupils  are  found 
inaccurate  and  unskilled  in  mechanical  processes,  review  the  work 
found  at  the  bottom  of  each  page  from  page  9  to  page  229.  Insist 
upon  absolute  accuracy- 


ID  d:DO^d 


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